Chapter 8
5. 11y 9 5y 15
Chapter Opener
6y 9 15
Math in the Real World (p. 399)
6y 9 9 15 9
The bike trail that rises 15 feet over a horizontal distance of
100 feet is steeper. Sample answer: Make a ratio of vertical
change to horizontal change for each trail.
6y 24
6y
24
6
6
15
3
First trail: 100 20
rise
horizontal change
2.5
5
rise
Second trail: 20
40
horizontal change
So, the first trail rises 3 feet over a horizontal distance of
20 feet and the second trail rises 2.5 feet over a horizontal
distance of 20 feet. So, the first trail is steeper.
y 4
Check:
11y 9 5y 15
11(4) 9 5(4) ⱨ 15
15 15 ✓
6. 29 4( f 2) 7
29 4 f 8 7
Prerequisite Skills Quiz (p. 400)
4 f 37 7
4 f 37 37 7 37
1. Sample answer: An equation is a mathematical sentence
formed by placing an equal sign between two
expressions, while an inequality is a mathematical
sentence formed by placing an inequality symbol (>, <, ≥,
or ≤) between two expressions. While a solution of an
equation like 5x 1 6 is a single number, the solution
of an inequality like 5x 1 > 6, 5x 1 < 6, 5x 1 ≥
6, or 5x 1 ≤ 6 is all numbers greater or less than a
number, and may or may not include the number itself.
2. Let x the cost of the trip.
Cost of the trip Difference in amounts Amount saved
x 62 156
4 f 44
4f
44
4
4
f 11
Check:
29 4( f 2) 7
29 4(11 2) ⱨ 7
7 7 ✓
7. x < 1
8. x ≥ 5
x 14 < 25
9.
x 14 14 < 25 14
x 62 62 156 62
x < 11
x 218
The trip costs $218.
3.
4(7 2t) 4
6
9
10
11
12
5y 150
≥ 5
5
28 8t 28 4 28
8t 24
y ≥ 30
8t
24
8
8
t3
4(7 2t) 4
4[7 2(3)] ⱨ 4
40
11.
44 ✓
4.
8
10. 5y ≤ 150
28 8t 4
Check:
7
18 3w 3
15 3w
15
3w
3
3
5 w
0
n
≥ 11
3
n
3 p ≥ 3 p 11
3
n ≥ 33
18 3(w 1)
18 3 3w 3 3
20
30
12.
31
32
33
34
35
36
29
30
m 6 > 21
m 6 6 > 21 6
m > 27
24
25
26
27
28
Check: 18 3(w 1)
18 ⱨ 3(5 1)
18 18 ✓
Copyright © Holt McDougal
All rights reserved.
LAHPA11FLSOL_c08.indd 273
Pre-Algebra
Chapter 8 Solutions Key
273
2/4/09 12:49:39 PM
Chapter 8 continued
Lesson 8.1
5.
y (1, 5)
5
4
8.1 Checkpoint (pp. 401–402)
3
(1, 2)
1
or x-coordinates. The range is the set of all outputs,
or y-coordinates.
3 2
O
2. The domain of the relation is the set of all inputs,
or x-coordinates. The range is the set of all outputs,
or y-coordinates.
Domain: 3, 1, 6
1
y
Input
4
(0, 3)
3
2
2
(5, 4)
0
1
2
4
5
(1, 2)
1
O
1
2
3
4
6.
3
4
3
4
5 x
y
(4, 8)
8
7
6
5
4
(0, 3)
3
5
6 x
Output
(4, 2)
1
Input
4
2
0
2
4
(2, 3)
Output
2
3
8
(2, 2)
2
3
4 3 2
O
1
2
3
4 x
4
(2, 1)
2
2
(4, 1)
The relation is not a function because the input 1 is paired
with two outputs, 2 and 5.
Range: 1, 0, 2, 4
(4, 4)
1
2
3
4
5
3
Range: 1, 4, 7
5
1
2
Domain: 0, 2, 3, 5
3.
Output
2
2
1. The domain of the relation is the set of all inputs,
Input
(2, 4)
(3, 3)
The relation is a function because every input is paired
with exactly one output.
3
7. Sample answer: The relation (1, 5), (2, 5), (3, 6),
(4, 11) is a function because every input is paired with
exactly one output.
The relation is a function because every input is paired
with exactly one output.
4.
y
4
3
2
1
4 3 2
(2, 3)
Input
Output
2
4
1
2
3
(0, 2)
O
1
2
0
3
2
4 x
(2, 1)
8.1 Practice and Problem Solving (pp. 404–406)
8. Domain: 2, 1, 0, 1
(3, 0), (4, 1), and (4, 0).
Domain: 4, 3, 2, 4
Range: 1, 0
The relation is not a function because the input 2 is
paired with two outputs, 4 and 1.
11. The relation consists of the ordered pairs (1.5, 4.3),
(1.5, 6.5), (2.8, 4.3), (2.8, 3.9), and (6.5, 0.2).
Domain: 1.5, 2.8, 6.5
8.1 Guided Practice (p. 403)
1. A relation is a function if for each input there is exactly
one output.
Input
1
0
2
y
6
5
4
3
1
4
(3, 4)
(4, 3)
(1, 2)
(2, 1)
(3, 0)
2
1
Sample answer: Each element of the domain can be
paired with either or both of the elements of the range.
Range: 0, 2, 4, 6, 8
274
Range: 0.2, 3.9, 4.3, 6.5
12. A relation is sometimes a function.
13.
Output
3. Domain: 0, 1, 2, 3, 4
4. Domain: 5, 1, 2, 7
Range: 3, 2, 5
Pre-Algebra
Chapter 8 Solutions Key
LAHPA11FLSOL_c08.indd 274
Range: 3, 6, 9
10. The relation consists of the ordered pairs (4, 0), (2, 1),
2
3
(2, 4)
4
2.
9. Domain: 3, 7
Range: 9, 2, 4, 5
2
O
1
2
3
4
5
Input
Output
1
0
1
2
3
4
2
3
4
6 x
2
The relation is not a function because the input 3 is paired
with two outputs, 0 and 4.
Copyright © Holt McDougal
All rights reserved.
2/4/09 12:49:41 PM
Chapter 8 continued
y
8
6
4
(4, 2)
(0, 4)
2
6 4
(2, 0)
O
2
4
(8, 0)
6
8 10 x
(6, 4)
4
6
8
Input
Output
4
0
2
6
8
4
0
2
4
15.
y
2
1
O
1
2
3
4 x
(1, 3)
(2, 3) 2
(2, 3)
(0, 3)
4
5
6
(1, 3)
Input
Output
2
1
0
1
2
3
20
10
20
15
(0, 15)
10
5
O
5 10 15 20 x
(10, 5)
(5, 10)
20
Input
Output
10
15
10
5
15
20
5
0
5
(5, 15)
represent a function because each age is paired with
exactly one height.
b. No. Sample answer: The ordered pairs (height, age)
do not represent a function because some heights will
be paired with more than one age. This is because the
height of an adult remains the same for many years.
18. The relation is not a function because the vertical line
x 1 passes through more than one point.
19. The relation is a function because no vertical line passes
through more than one point.
20. The relation is not a function because the vertical lines
x 0, x 1, and x 2 pass through more than one point.
21. a. Domain: 62, 73, 81, 82
Range: 604, 1086, 1102, 1199, 1208
Input
Output
62
604
1086
1102
1199
1208
81
82
The reading on the skydiver’s altimeter decreases.
b. The domain of the relation is the altitude of the
skydiver. The range of the relation is the atmospheric
pressure at each altitude.
to only one atmospheric pressure output. The relation
also passes the vertical line test.
trigger the alarm.
17. a. Yes. Sample answer: The ordered pairs (age, height)
73
relation is a function. Sample answer: It can quickly be
determined how many outputs an input is paired with.
d. An atmospheric pressure of about 1900 lb/ft2 will
The relation is not a function because the input 10 is
paired with two outputs, 5 and 20.
b.
23. The mapping diagram more clearly shows whether a
25. Sample answer: The relation (1, 3), (2, 3), (1, 5),
y
(10, 20)
b. Opal qualified as a hurricane for advisories 20 –30.
c. Yes. Sample answer: Each altitude input corresponds
The relation is a function because every input is paired
with exactly one output.
16.
can be paired with only one wind speed output. The
relation also passes the vertical line test.
24. a. As a skydiver falls, the atmospheric pressure increases.
The relation is a function because every input is paired
with exactly one output.
4 3 2
22. a. Yes. Sample answer: Each advisory number input
(4, 6) is a function because each input is paired with
exactly one output. The inverse (3, 1), (3, 2), (5, 1),
(6, 4) is not a function because the input 3 is paired with
two outputs, 1 and 2.
26. a.
Cowbird Growth
Mass (grams)
14.
40
36
32
Vireo
28
24
20
16
Gnatcatcher
12
8
4
0
0 2 4 6 8 10 12 14 16
Age (days)
b. Sample answer: The growth is the same in that for
both the vireo and the gnatcatcher, the cowbird’s
growth is not too fast the first two days, then is more
rapid the next several days before slowing and almost
stopping. It is different in that the growth for the
cowbird raised by the gnatcatcher decreases and levels
off with the cowbird at an earlier stage and at a much
lower mass than the cowbird raised by the vireo.
8.1 Mixed Review (p. 406)
27. When x 5 and y 7; x y 5 (7) 12
28. When x 5 and y 7;
y x 10 7 (5) 10
7 5 10
2 10
8
29. When x 5 and y 7;
2x 2y 2(5)2(7) 2(25)(7) 50(7) 350
c. No; the relation is not a function because the input 82
is paired with two outputs, 1102 and 1208.
Copyright © Holt McDougal
All rights reserved.
LAHPA11FLSOL_c08.indd 275
Pre-Algebra
Chapter 8 Solutions Key
275
2/4/09 12:49:44 PM
Chapter 8 continued
30. When x 5 and y 7; 3x 4y 3(5) 4(7)
5. y 2x
15 (28)
x
2
1
0
1
2
15 28
y
4
2
0
2
4
13
31.
(2, 4), (1, 2), (0, 0), (1, 2), (2, 4)
x 11 3
8 11 ⱨ 3
y
4
3
33 ✓
2
So, 8 is a solution.
32.
1
17 a 23
17 (6) ⱨ 23
4 3 2
2
3
4 x
2
17 6 ⱨ 23
3
4
11 23
So, 6 is not a solution.
33.
1
O
6. y x 3
6m 84
6(13) ⱨ 84
78 84
x
2
1
0
1
2
y
5
4
3
2
1
(2, 5), (1, 4), (0, 3), (1, 2), (2, 1)
So, 13 is not a solution.
144
u
144 ⱨ
12
12
34. 12
y
5
4
3
2
1
12 12 ✓
3 2
So, 12 is a solution.
O
1
2
3
5 x
4
2
3
35. I Prt (850)(0.03)(6) 153
$850 $153 $1003
The interest is $153, and the balance is $1003.
36. I Prt (4200)(0.05)(7.5) 1575
$4200 $1575 $5775
The interest is $1575, and the balance is $5775.
7. y 3x 4
x
2
1
0
1
2
y
10
7
4
1
2
(2, 10), (1, 7), (0, 4), (1, 1), (2, 2)
8.1 Standardized Test Practice (p. 406)
y
2
1
37. a. Yes. Sample answer: Each merchandise cost input is
paired with exactly one shipping cost output.
b. No. Sample answer: Each shipping cost input is
paired with many merchandise costs output.
Lesson 8.2
4 3 2
O
2
3
4 x
2
3
4
8.2 Checkpoint (pp. 407–409)
3x 2y 8
1.
3x 2y 8
2.
3(0) 2(4) ⱨ 8
3(2) 2(1) ⱨ 8
8 8
8 8 ✓
(2, 1) is a solution.
(0, 4) is not a solution.
3x 2y 8
3.
3(4) 2(12) ⱨ 8
3x 2y 8
4.
3(10) 2(19) ⱨ 8
12 8
(4, 12) is not a solution.
276
8 8 ✓
(10, 19) is a solution.
Pre-Algebra
Chapter 8 Solutions Key
LAHPA11FLSOL_c08.indd 276
Copyright © Holt McDougal
All rights reserved.
2/4/09 12:49:46 PM
Chapter 8 continued
1
8. y 2 x 1
5.
x
4
2
0
2
4
y
1
0
1
2
3
y 5x 7
14 ⱨ 5(4) 7
6.
y 5x 7
22 ⱨ 5(3) 7
14 13
22 22 ✓
(4, 14) is not a solution.
(3, 22) is a solution.
7. y x 4
(4, 1), (2, 0), (0, 1), (2, 2), (4, 3)
y
4
3
x
2
1
0
1
2
y
6
5
4
3
2
2
(2, 6), (1, 5), (0, 4), (1, 3), (2, 2)
4
2
O
1
2
3
4 x
y
2
2
1
3
4
9.
2
x4
2
1
O
2
3
4
2
3
5
6 x
3
4
5
6 x
1
2
3
4 x
1
2
3
4 x
8. x 1
y 1
y
2
1
The horizontal line y 1 is a function. The vertical line
x 4 is not a function.
10. 2x 3y 3
4 3 2
O
9. y 2
3y 2x 3
y
2
3
y 3x 1
1
x
6
3
0
3
6
y
5
3
1
1
3
4 3 2
O
10. 3x 2y 2
y
4
3
2y 3x 2
2
y 2x 1
3
1
4 3 2
2
6
1
2
1
2
3
y
4
3
O
O
2
3
4 x
2
3
x
4
2
0
2
4
y
5
2
1
4
7
4
y
4
3
2
8.2 Guided Practice (p. 410)
1
1. An equation whose graph is a line is called a
4 3 2
linear equation.
2. No. Sample answer: The equation x 4y 3 is not in
function form because the equation is solved for x, not y.
1
3
The equation in function form is y 4x 4.
3. y 5x 7
3 ⱨ 5(2) 7
2
3
4 x
y 5x 7
0 ⱨ 5(0) 7
33 ✓
6 7
(2, 3) is a solution.
(0, 6) is not a solution.
Copyright © Holt McDougal
All rights reserved.
LAHPA11FLSOL_c08.indd 277
4.
1
2
3
4
Pre-Algebra
Chapter 8 Solutions Key
277
2/4/09 12:49:48 PM
Chapter 8 continued
11. (1) d 24t
17. y 2x 3
t
0
5
10
15
20
25
30
x
2
1
0
1
2
d
0
120
240
360
480
600
720
y
7
5
3
1
1
(2)
y
Distance (m)
Sojourner Trip
3
d
700
600
500
400
300
200
100
0
2
1
3 2
O
1 2 3 4 5 x
2
3
5
5 10 15 20 25 30 35 t
Time (h)
0
The equation is a function.
(3) 500 24t
18. y 1
500
24t
24
24
y
4
3
20.8 ≈ t
2
It would take Sojourner about 21 hours to reach its
maximum distance from the lander.
4 3 2
O
yx3
4 ⱨ 1 3
y 4x 9
3 ⱨ 4(3) 9
13.
4 2
3 3 ✓
(1, 4) is not a solution.
14.
x 2y 8
6 2(7) ⱨ 8
(3, 3) is a solution.
88 ✓
(9, 5) is not a solution.
y
4
3
2
1
6 5
3 2
O
2
1
0
1
2
y
2
1
0
1
2
The equation is not a function.
3
1
O
2 x
20. y 2x 1
y
4
3
2
4 3 2
1
2
3
4
16. y x
x
4 x
The equation is a function.
2 1
(6, 7) is a solution.
3
19. x 4
3x 5y 1
3(9) 5(5) ⱨ 1
15.
2
2
3
4
8.2 Practice and Problem Solving (pp. 410–412)
12.
1
1
2
3
x
4
2
0
2
4
y
5
2
1
4
7
4 x
y
2
3
4
The equation is a function.
3
2
1
5 4 3 2
O
1 2 3 x
2
3
4
5
The equation is a function.
278
Pre-Algebra
Chapter 8 Solutions Key
LAHPA11FLSOL_c08.indd 278
Copyright © Holt McDougal
All rights reserved.
2/4/09 12:49:50 PM
Chapter 8 continued
21. y 5
25. 2x y 1
y 2x 1
y
1
4 3 2
O
1
2
3
4 x
2
x
2
1
0
1
2
y
5
3
1
1
3
3
4
y
4
3
6
7
1
4 3 2
The equation is a function.
y
4
3
2
2
3
4 x
26. 3x y 5
1
O
1
2
3
4
22. x 3
2
O
y 3x 5
1
4
2
5
6 x
y 3x 5
2
3
4
x
2
1
0
1
2
y
11
8
5
2
1
The equation is not a function.
y
23. y 5x 2
2
1
x
2
1
0
1
2
y
12
7
2
3
8
4 3 2
O
1
2
3
4 x
2
3
4
5
y
3
2
1
4 3 2
27. 8x 2y 4
O
1
2
3
4 x
2y 8x 4
2
3
4
y 4x 2
The equation is a function.
x
2
1
0
1
2
y
6
2
2
6
10
24. y x 1
y
yx1
x
y
3
2
2
1
0
3
2
1
1
0
1
2
1
4 3 2
O
1
2
3
4 x
2
3
4
5
y
4
3
2
1
4 3 2
O
1
2
3
4 x
2
3
4
Copyright © Holt McDougal
All rights reserved.
LAHPA11FLSOL_c08.indd 279
Pre-Algebra
Chapter 8 Solutions Key
279
2/4/09 12:49:52 PM
Chapter 8 continued
28. x 3y 9
31. 2x 3y 12
3y x 9
1
x
3
y
3y 2x 12
2
y 3x 4
3
x
6
3
0
3
6
x
6
3
0
3
6
y
1
2
3
4
5
y
8
6
4
2
0
1 2 3 4 5 6
x
y
8 7 6 5 4 3 2
y
5
4
6
5
2
3
1
2
O
1
x
O
2
3
2
29. 3x 4y 0
32. y 2000x 2000(195) 390,000
4y 3x
y
The weight of the whale is 390,000 pounds.
33. y 0.001x 0.001(355) 0.355
3
4x
The capacity of the can is 0.355 liter.
x
8
4
0
4
8
y
6
3
0
3
6
34. y ≈ 2.59x 2.59(56,276) 145,754.84 ≈ 146,000
Iowa has an area of about 146,000 square kilometers.
35. y 2x 5
y
4
3
2
a 2(1) 5
a 2 5
1
4 3 2
a3
O
2
3
4 x
36.
2
3
4
5 1 3a 1 1
6 3a
30. 5x 2y 6
6
3a
3
3
2y 5x 6
5
y 2x 3
2 a
x
4
2
0
2
4
y
13
8
3
2
7
37.
16 7a 19
16 7a 16 19 16
3
2
7a 35
7a
35
7
7
1
O
4x 7y 19
4(4) 7a 19
y
4 3 2
y 3x 1
5 3a 1
2
3
4 x
2
3
a 5
38.
6x 5y 21
6(a 2) 5(3) 21
6a 12 15 21
6a 3 21
6a 3 3 21 3
6a 24
6a
24
6
6
a4
280
Pre-Algebra
Chapter 8 Solutions Key
LAHPA11FLSOL_c08.indd 280
Copyright © Holt McDougal
All rights reserved.
2/4/09 12:49:54 PM
Chapter 8 continued
39. a. f 0.560t 17.7
42. a. y x 2
0.560(250) 17.7
140 17.7
157.7
The fork length of the bigeye thresher is about
158 centimeters.
f 0.776t 0.313
0.776(250) 0.313
194 0.313
193.687
The fork length of the scalloped hammerhead is about
194 centimeters.
f 0.944t 5.74
0.944(250) 5.74
236 5.74
230.26
The fork length of the white shark is about
230 centimeters.
158
0.632 ≈ 63%
b. Bigeye thresher: 250
x
3
2
1
0
1
2
3
y
9
4
1
0
1
4
9
b.
(3, 9) y
7
6
(2, 4)
4 3 2
(1, 1)
(0, 0)
1
O
1
2
3
4 x
equation because the graph is a curve, not a straight
line. y x 2 is a function because its graph passes the
vertical line test.
8.2 Mixed Review (p. 412)
43.
2x 5 7
2x 5 5 7 5
2x 12
230
0.92 92%
White shark: 250
2x
12
2
2
c. Bigeye thresher. Sample answer: The bigeye thresher
x 6
has the shortest body relative to its total length, so it
must have the longest tail relative to its body length.
Check:
40. a. a 0.0129d 2.25
2x 5 7
2(6) 5 ⱨ 7
7 7 ✓
44.
5c 8 27
5c 8 8 27 8
5c 35
a 0.0129d 2.25
27.7 0.0129d 2.25
27.7 2.25 0.0129d 2.25 2.25
29.95 0.0129d
0.0129d
29.95
0.0129
0.0129
2321.71 ≈ d
Midway is about 2320 kilometers from Kilauea.
41. a.
f 2.13s 1.19
f 1.19 2.13s 1.19 1.19
f 1.19 2.13s
f 1.19
2.13s
2.13
2.13
f 1.19
s
2.13
f 1.19
b. s 2.13
(2, 4)
3
c. No; yes. Sample answer: y x 2 is not a linear
194
b.
5
4
2
(1, 1)
0.776 ≈ 78%
Scalloped hammerhead: 250
0.0129(4794) 2.25
61.8426 2.25
59.5926
Suiko is about 59.6 million years old.
(3, 9)
8
5c
35
5
5
c7
Check:
5c 8 27
5(7) 8 ⱨ 27
27 27 ✓
45.
4 3w 16
4 3w 4 16 4
3w 12
3w
12
3
3
w 4
Check:
4 3w 16
4 3(4) ⱨ 16
16 16 ✓
3 1.19 1.81
s ≈ 0.8
2.13
2.13
The speed of the platypus is about 0.8 meter
per second.
Copyright © Holt McDougal
All rights reserved.
LAHPA11FLSOL_c08.indd 281
Pre-Algebra
Chapter 8 Solutions Key
281
2/4/09 12:49:56 PM
Chapter 8 continued
n
2 9
6
46.
3. y 2.5x 6
n
2 2 9 2
6
n
7
6
n
6 p 6 p 7
6
4. y 0.5x 4
Y1=-2.5X+6
Y1=-.5x+4
X=3.2
X=-2.4
Y=-2
(3.2, 2)
n 42
Y=5.2
(2.4, 5.2)
5. C 15 3.25g
n
Check: 2 9
6
42
2 ⱨ 9
6
y 15 3.25x
Y1=15+3.25X
99 ✓
3
1
4
1
4
12
1p冫
冫4 p 1
12
1
47. 25% of 12 p 12 p 3
X=9
Y=44.25
1
8
(9, 44.25)
9
9 80
9p冫
80
48. 90% of 80 p 80 p 72
10
10 1
冫
10 p 1
You can rent 9 games for $44.25.
1
35
3
3 140
3 p 1冫
40
49. 75% of 140 p 140 p 105
4
4
1
冫4 p 1
Lesson 8.3
8.3 Checkpoint (p. 415)
1
5
1.
38
38 500
38 p 5冫
00
50. 38% of 500 p 500 p 190
100
100
1
1冫
00 p 1
x 2y 2
x 2y 2
x 2(0) 2
0 2y 2
x 2
2y 2
1
51. Domain: 2, 0, 2, 4
Range: 1, 2, 3, 4
52. Domain: 7, 5
y1
The x-intercept is 2, and the y-intercept is 1.
Range: 0, 3, 8
53. Domain: 6
54. Domain: 1, 2, 3, 4
Range: 2, 1, 4, 9
y
4
3
2
Range: 1, 8, 27, 64
8.2 Standardized Test Practice (p. 412)
55. B;
(2, 0)
5x 4y 7
5(5) 4(9) ⱨ 7
4
(0, 1)
2
O
11 7
(5, 9) is not a solution.
2.
56. I
8.2 Technology Activity (p. 413)
1. y 5 x
1
2
3
4 x
2
3
4
4x 3y 12
4x 3y 12
4x 3(0) 12
4(0) 3y 12
4x 12
3y 12
x3
y4
2. y x 5
The x-intercept is 3, and the y-intercept is 4.
Y1=X-5
Y1=5-X
y
6
5
X=1.8
X=2.8
Y=3.2
Y=-2.2
4
(0, 4)
3
2
(1.8, 3.2)
(2.8, 2.2)
1
2
O
(3, 0)
1
2
3
4
5
6 x
2
282
Pre-Algebra
Chapter 8 Solutions Key
LAHPA11FLSOL_c08.indd 282
Copyright © Holt McDougal
All rights reserved.
2/4/09 12:49:58 PM
Chapter 8 continued
3.
y 2x 8
y 2x 8
0 2x 8
y 2(0) 8
amount of chicken.
y 8
Cost of Amount
Total
Cost of Amount
ground p of ground p
cost
chicken of chicken
beef
beef
2x 8
9. Let x the amount of ground beef, and let y the
x 4
The x-intercept is 4, and the y-intercept is 8.
(4, 0)
3x 5y 30
y
6 5 4 3 2
O
1 2 x
2
3
3x 5y 30
3x 5y 30
3x 5(0) 30
3(0) 5y 30
3x 30
5y 30
x 10
y6
4
5
6
Barbecue Food
(0, 8)
y
7
Chicken (lb)
8
8.3 Guided Practice (p. 416)
1. For the line that passes through the points (0, 7) and
(3, 0), the y-intercept is 7 and the x-intercept is 3.
2. Sample answer: To find the x-intercept, substitute 0 for
6
5
4
3
2
1
0
y in the equation and solve for x. To find the y-intercept,
substitute 0 for x in the equation and solve for y.
(0, 6)
(10, 0)
0
2
4
6
8 10
Ground beef (lb)
x
3. The x-intercept is 3, and the y-intercept is 2.
8.3 Practice and Problem Solving (pp. 416–418)
4. The x-intercept is 2, and the y-intercept is 4.
10. 5x y 5
5x y 5
5x 0 5
5(0) y 5
5x 5
y5
5. The x-intercept is 0, and the y-intercept is 0.
6.
y
6
(0, 5)
5
x1
4
3
2
The x-intercept is 1, and the y-intercept is 5.
y
1
2
O
(4, 0)
1
2
3
4
5
5
4
3
2
1
6 x
2
7.
y
4 3 2
5
11.
1
O
1 x
x 2(0) 4
0 2y 4
x4
2y 4
y 2
The x-intercept is 4, and the y-intercept is 2.
y
4
3
(1, 0)
y
3
2
2
1
O
2
3
4
1
1
2
3
4 x
2
O
(0, 2)
Copyright © Holt McDougal
All rights reserved.
LAHPA11FLSOL_c08.indd 283
4 x
x 2y 4
3
4 3 2
3
x 2y 4
2
8.
2
2
2
6 5 4 3 2
(1, 0)
O
(0, 3)
(6, 0)
(0, 5)
3
4
5
(4, 0)
1
2
4
5
6 x
(0, 2)
Pre-Algebra
Chapter 8 Solutions Key
283
2/4/09 12:50:00 PM
Chapter 8 continued
3x 2y 6
3x 2y 6
3x 2(0) 6
3(0) 2y 6
3x 6
2y 6
x 2
y3
12.
15. ––CONTINUED––
y
7
(0, 6)
5
4
3
The x-intercept is 2, and the y-intercept is 3.
2
(9, 0)
y
1
5
4
3
8 7 6 5 4 3 2
2
1
(2, 0)
5 4 3
y 2x 4
16.
O
1
3 x
2
y 2(0) 4
2x 4
y 4
x2
4x 5y 20
4x 5y 20
4x 5(0) 20
4(0) 5y 20
4x 20
5y 20
x 5
y 4
The x-intercept is 2, and the y-intercept is 4.
y
2
1
3 2
The x-intercept is 5, and the y-intercept is 4.
4
1
(5, 0)
3 2
O
(2, 0)
O
1 2 3 4 5 x
2
3
y
7 6 5
x
y 2x 4
0 2x 4
2
3
13.
O
( 0, 3)
1 x
(0, 4)
6
2
3
(0, 4)
17. y x 7
y x 7
0 x 7
y 0 7
x7
y7
5
6
7
The x-intercept is 7, and the y-intercept is 7.
4x 3y 24
4x 3y 24
4x 3(0) 24
4(0) 3y 24
4x 24
3y 24
x6
y8
14.
y
(0, 7)
6
5
4
3
The x-intercept is 6, and the y-intercept is 8.
2
1
(7, 0)
y
8
(0, 8)
O
1 2 3 4 5 6 7 8 x
7
6
18.
5
4
3
2
0 3x 9
y 3(0) 9
1
2
3
4
5
6
y9
x 3
( 6, 0 )
7 x
The x-intercept is 3, and the y-intercept is 9.
2x 3y 18
2x 3y 18
2x 3(0) 18
2(0) 3y 18
2x 18
3y 18
x 9
y6
15.
y 3x 9
3x 9
1
O
y 3x 9
y
9
7
6
5
4
3
2
1
The x-intercept is 9, and the y-intercept is 6.
––CONTINUED––
(3, 0)
6 5 4
284
Pre-Algebra
Chapter 8 Solutions Key
LAHPA11FLSOL_c08.indd 284
(0, 9)
2
O
1 2 x
Copyright © Holt McDougal
All rights reserved.
2/4/09 12:50:02 PM
Chapter 8 continued
19. a. Let x the amount of canned food, and let y the
20. ––CONTINUED––
amount of dry food.
9
1
4
1
4
y 18 2x
4.5 18 2x
40x 100y 800
40x 100y 800
13.5 2x
40x 100(0) 800
40(0) 100y 800
40x 800
100y 800
13.5 2x
2
2
x 20
y8
3
6 x
4
The x-intercept is 20, and the y-intercept is 8.
3
Dry food (oz)
y
12
10
(0, 8)
8
6
4
(20, 0)
2
0
0 2 4 6 8 10 12 14 16 18 20 x
Canned food (oz)
21.
1.9x 1.9y 3.8
1.9x 1.9y 3.8
1.9x 1.9(0) 3.8
1.9(0) 1.9y 3.8
1.9x 3.8
1.9y 3.8
x2
y
3
2
1
canned food, and 8 ounces dry food, or 10 ounces
canned food and 4 ounces dry food, or 20 ounces
canned food and 0 ounce dry food.
3 2
y 18 2x
3
4
0 18 2x
y 18 2(0)
5
y 18
22.
The x-intercept is 9, and the y-intercept is 18.
Gas remaining (gal)
2
3
4
5 x
(0, 2)
2.1x 3.5y 10.5
2.1x 3.5(0) 10.5
2.1(0) 3.5y 10.5
2.1x 10.5
3.5y 10.5
x5
y3
The x-intercept is 5, and the y-intercept is 3.
y
14
12
10
8
6
5
4
3
2
1
4
2
0
1
2.1x 3.5y 10.5
A Tank of Gas
y
(0, 18)
18
16
(2, 0)
O
y 18 2x
x9
y 2
The x-intercept is 2, and the y-intercept is 2.
c. Sample answer: You can feed your beagle 0 ounce
2x 18
1
After 6 4 hours of driving, 4 tank of gas is left.
Beagle Food
20. a.
9
2
2
40x 100y 800
b.
1p冫
18
冫4 p 1
18
1
c. (18) p 4.5
Calories Amount
Amount
Calories
Total
in canned p of canned in dry p of dry calories
food
food
food
food
(0, 3)
( 5, 0)
(9, 0)
O
0 1 2 3 4 5 6 7 8 9 x
Driving time (h)
––CONTINUED––
2
3
4
5
7 x
2
3
b. Sample answer: The x-intercept represents the number
of hours until the fuel tank is empty. The y-intercept
represents the amount of fuel the tank can hold.
1
23.
y 1.5x 6
y 1.5x 6
0 1.5x 6
y 1.5(0) 6
1.5x 6
y6
x 4
The x-intercept is 4, and the y-intercept is 6.
––CONTINUED––
Copyright © Holt McDougal
All rights reserved.
LAHPA11FLSOL_c08.indd 285
Pre-Algebra
Chapter 8 Solutions Key
285
2/4/09 12:50:04 PM
Chapter 8 continued
23.––CONTINUED––
26. ––CONTINUED––
y
y
2
7
3 2
4
3
3 2
2
3
4
5 x
7
2
O
1
2 x
6
2
y 7x 2
2
2
y 7(0) 2
y 7x 2
2
0 7x 2
2
x
7
3
2
1
(0, )
1
6 5
24.
O
2
3
2
(4, 0)
( , 0)
1
6
(0, 6)
5
y 2
2
27. Sample answer: y 5 has no x-intercept. It is a
horizontal line with y-intercept 5.
x 2 has no y-intercept. It is a vertical line with
x-intercept 2.
28. The line slants upward from left to right.
x 7
Sample graph:
y
The x-intercept is 7, and the y-intercept is 2.
y
3
O
2
(7, 0)
7
4 3 2
O
1 x
(0, 2)
29. a. Let x the number of hours for single-engine
airplanes, and let y the number of hours for
twin-engine airplanes.
4
5
1
x
2
25.
1
x
2
1
3
1
x
2
4y 2
3
1
(0)
2
4y 2
4y 2
1
4(0) 2
1
x
2
3
2
1
3
1
3
1
y
4
3
2
x3
Hours for Cost for Hours
Cost for
Total
single- p single- twin- p for twin- fees
engine
engine
engine
engine
60x 180y 9000
b.
y6
60x 180y 9000
60x 180y 9000
60x 180(0) 9000
60(0) 180y 9000
60x 9000
180y 9000
x 150
y 50
The x-intercept is 3, and the y-intercept is 6.
y
The x-intercept is 150, and the y-intercept is 50.
(0, 6)
Airplane Rental
Twin-engine (h)
6
5
4
3
2
1
3 2
(3, 0)
O
1
2
3
5 x
7
y 3x 2
7
7
7
y 3(0) 2
7
7
7
0 3x 2
7
7
7
3x 2
x
4
7
y 3x 2
26.
y 2
30
15
0
(150, 0)
0
30
60
90
120
Single-engine (h)
150 x
c. The single-engine planes must be rented for 60 hours.
d.
60x 180y 9000
60x 5400 9000
3
––CONTINUED––
Pre-Algebra
Chapter 8 Solutions Key
LAHPA11FLSOL_c08.indd 286
y
75
60 (0, 50)
45
60x 180(30) 9000
3
2
7
The x-intercept is 2, and the y-intercept is 2.
286
x
1
60x 5400 5400 9000 5400
60x 3600
x 60
Copyright © Holt McDougal
All rights reserved.
2/4/09 12:50:06 PM
Chapter 8 continued
30. a. P 2l 2w
32. ––CONTINUED––
16 2x 2y
Decreasing Distance
16 2x 2y
16 2x 2(0)
16 2(0) 2y
16 2x
16 2y
8x
8y
Walking time (h)
b. 16 2x 2y
The x-intercept is 8, and the y-intercept is 8.
Rectangle Dimensions
Width (in.)
y
9
(0, 8)
8
7
6
5
4
3
2
1
0
Running time (h)
b. Sample answer: The y-intercept stays the same, but
the x-intercept moves closer to the origin, resulting in
the graph getting steeper.
(8, 0)
0 1 2 3 4 5 6 7 8 9 x
Length (in.)
c. Sample answer: The x-intercept stays the same, but
the y-intercept moves closer to the origin, resulting in
the graph getting less steep.
c. Sample answer: x 3 and y 5, x 4 and y 4,
x 7 and y 1
d. Sample answer: Both the x- and y-intercepts move
d. No. Sample answer: The x- and y-intercepts do not
represent possible side lengths. For the x-intercept,
y 0 and for the y-intercept, x 0, and neither the
length nor the width of a rectangle can be 0.
31. Sample answer: 4x 6y c
farther from the origin together in such a way that
the steepness of the line does not change for
different distances.
33.
ax b
b
x a
32. a. r increases.
Walking time (h)
Increasing Running Speed
b
The x-intercept is .
a
y
(0, 9)
9
8
3x 2y 18
7
6
6x 2y 18
5
4
9x 2y 18
3
y ax b
y a(0) b
yb
The y-intercept is b.
2
1
(2, 0)
(3, 0)
(6, 0)
0
0 1 2 3 4 5 6 7 8 9 x
y 3x 12
b
12
4
a
3
Running time (h)
b 12
w increases.
The x-intercept is 4, and the y-intercept is 12.
Walking time (h)
Increasing Walking Speed
y
(0, 9)
9
8
9x 2y 18
7
(0, 6)
9x 6y 18
36.
(2, 0)
d increases.
––CONTINUED––
Copyright © Holt McDougal
All rights reserved.
8 (1)
81
9
41
41
3
3 (5) 3 5
2
1
68
68
2
4 24
4 (24)
20
5
95
95
4
7 (11)
18
7 11
2
12 (3)
12 3
9
52 40
12
Amount of increase
increase; 30%
40
40
Amount of original
34. 3
35.
Running time (h)
LAHPA11FLSOL_c08.indd 287
8.3 Mixed Review (p. 418)
9x 3y 18
(0, 3)
0 1 2 3 4 5 6 7 8 9 x
y ax b
0 ax b
Let c 12, 24, and 36. The intercepts are common
multiples of the coefficients of x and y.
6
5
4
3
2
1
0
y
(0, 12)
12
11
(0, 9)
10
9
6x 2y 24
8
(0, 6)
7
6
6x 2y 18
5
4
6x 2y 12
3
2
(3, 0)
1
(2, 0)
(4, 0)
0
0 1 2 3 4 5 6 7 8 9 x
37.
38.
Pre-Algebra
Chapter 8 Solutions Key
287
2/4/09 12:50:08 PM
Chapter 8 continued
Amount of increase
Amount of original
111 60
60
51
60
Amount of decrease
Amount of original
78 39
78
39
78
39. increase; 85%
48. ––CONTINUED––
Car Washes
41. decrease;
55
250 195
Amount of decrease
22%
250
250
Amount of original
42.
y 2x 7
ⱨ
9 2(8) 7
9 9 ✓
Deluxe washes
40. decrease; 50%
y
90
(0, 80)
80
70
60
50
40
30
20
10
0
(120, 0)
0
20
40
(8, 9) is a solution.
43.
y 10x 4
10 ⱨ 10(0) 4
100 120 x
(0, 10) is not a solution.
Lesson 8.4
5x y 15
5(6) 15 ⱨ 15
8.4 Concept Activity (p. 419)
Investigate
15 15
Check student’s setup.
(6, 15) is not a solution.
45.
80
Sample answer: Three possible combinations are 0 basic
washes and 80 deluxe washes, 120 basic washes and 0
deluxe washes, or 60 basic washes and 40 deluxe washes.
10 4
44.
60
Basic washes
Draw Conclusions
3x 8y 12
3(4) 8(3) ⱨ 12
1. The steeper ramp has a larger slope than the other ramp.
2. When the slope is 1, the rise and run of a ramp are equal.
12 12 ✓
Let the rise and run of a ramp equal x.
(4, 3) is a solution.
8.3 Standardized Test Practice (p. 418)
46. B;
y 4x 32
0 4x 32
8.4 Checkpoint (pp. 421–422)
4x 32
x 8
rise
run
difference of y-coordinates
difference of x-coordinates
72
41
5
3
rise
2. m run
difference of y-coordinates
difference of x-coordinates
15
6 (2)
4
8
1
2
1. m The x-intercept is 8.
47. I;
rise
x
slope 1
run
x
3. When the rise increases and the run stays the same, the
slope increases.
5x 2y 30
5(0) 2y 30
2y 30
y 15
The y-intercept is 15.
48. Let x the number of basic washes, and let y the
number of deluxe washes.
Cost of Number
Cost of Number
Total
basic p of basic deluxe p of deluxe sales
washes
wash
washes
wash
8x 12y 960
8x 12y 960
8x 12y 960
8x 12(0) 960
8(0) 12y 960
8x 960
12y 960
x 120
y 80
The x-intercept is 120, and the y-intercept is 80.
––CONTINUED––
288
Pre-Algebra
Chapter 8 Solutions Key
LAHPA11FLSOL_c08.indd 288
Copyright © Holt McDougal
All rights reserved.
2/4/09 12:50:10 PM
Chapter 8 continued
rise
run
difference of y-coordinates
difference of x-coordinates
9 0
30
3. m rise
run
8. m difference of y-coordinates
difference of x-coordinates
15
41
9
3
4
3
3
4
3
rise
4. m run
difference of y-coordinates
difference of x-coordinates
80
75
8
2
4
rise
run
difference of y-coordinates
difference of x-coordinates
53
42
5. m 2
2
1
The slope is positive.
rise
run
6. m difference of y-coordinates
difference of x-coordinates
1 3
66
4
0
The slope is undefined.
rise
run
7. m difference of y-coordinates
difference of x-coordinates
44
5 (7)
0
12
The slope is negative.
8.4 Guided Practice (p. 423)
1. The vertical change between two points on a line is called
the rise, and the horizontal change is called the run.
2. Sample answer: The denominator of the slope ratio for a
vertical line is always 0 because the x-coordinate of every
point on a vertical line is the same, and division by 0 is
undefined.
3. Sample answer: The x- and y-coordinates need to be used
in the same order. If you subtract the second x-coordinate
from the first x-coordinate to obtain the denominator
5 0, then you should subtract the second y-coordinate
from the first y-coordinate to obtain the numerator 4 2.
42 2
So, m .
50 5
4. The slope is positive.
rise
m run
difference of y-coordinates
difference of x-coordinates
2 (1)
41
3
3
1
5. The slope is positive.
rise
m run
difference of y-coordinates
difference of x-coordinates
1 (3)
30
2
3
The slope is zero.
Copyright © Holt McDougal
All rights reserved.
LAHPA11FLSOL_c08.indd 289
Pre-Algebra
Chapter 8 Solutions Key
289
2/4/09 12:50:12 PM
Chapter 8 continued
11. y 2x 4
6. The slope is zero.
(0, 4), (1, 6)
rise
m run
rise
m run
difference of y-coordinates
difference of x-coordinates
64
10
2
1
difference of y-coordinates
difference of x-coordinates
22
2 (3)
0
5
0
rise
run
2
5
12
7. slope Sample answer:
5
12
12. y 1
0.416
苶 and
3
5
0.6, the ramp in
Example 1 has a greater slope. Therefore, it is steeper.
8.4 Practice and Problem Solving (pp. 423–425)
8. The slope is positive.
rise
m run
difference of y-coordinates
difference of x-coordinates
41
2 (2)
3
4
9. The slope is negative.
rise
m run
difference of y-coordinates
difference of x-coordinates
2 (1)
1 3
3
4
3
4
10. The slope is undefined.
rise
m run
difference of y-coordinates
difference of x-coordinates
3 (2)
1 (1)
5
0
290
Pre-Algebra
Chapter 8 Solutions Key
LAHPA11FLSOL_c08.indd 290
(0, 1), (4, 1)
rise
m run
difference of y-coordinates
difference of x-coordinates
1 (1)
40
0
4
0
3
2
13. y x 5
(0, 5), (2, 2)
rise
m run
difference of y-coordinates
difference of x-coordinates
2 (5)
20
3
2
14. x 2y 6
(0, 3), (2, 2)
rise
m run
difference of y-coordinates
difference of x-coordinates
23
20
1
2
1
2
Copyright © Holt McDougal
All rights reserved.
2/4/09 12:50:14 PM
Chapter 8 continued
rise
run
difference of y-coordinates
difference of x-coordinates
73
53
4
2
15. 4x 3y 12
22. m (3, 0), (0, 4)
rise
m run
difference of y-coordinates
difference of x-coordinates
4 0
03
4
3
4
3
2
rise
run
difference of y-coordinates
difference of x-coordinates
31
46
2
2
23. m 16. x 3
(3, 1), (3, 6)
rise
m run
difference of y-coordinates
difference of x-coordinates
61
33
5
0
1
rise
run
difference of y-coordinates
difference of x-coordinates
23
77
1
0
24. m The slope is undefined.
difference of y-coordinates
difference of x-coordinates
54 27
21
27
1
17. a. m The slope is undefined.
27
b. Sample answer: The cheetah’s speed in meters per
second.
c. Sample answer: It would also start at the origin,
but rise less steeply because the gazelle’s speed of
22 meters per second is less than the cheetah’s speed
of 27 meters per second, and the speed is indicated by
the slope.
18. Sample answer:
19. Sample answer:
y
O
y
x
20. Sample answer:
O
Copyright © Holt McDougal
All rights reserved.
LAHPA11FLSOL_c08.indd 291
x
21. Sample answer:
y
O
rise
run
difference of y-coordinates
difference of x-coordinates
11 (5)
6 (3)
6
9
2
3
rise
26. m run
difference of y-coordinates
difference of x-coordinates
81
12 4
7
8
25. m y
x
O
x
Pre-Algebra
Chapter 8 Solutions Key
291
2/4/09 12:50:16 PM
Chapter 8 continued
rise
run
difference of y-coordinates
difference of x-coordinates
7 (7)
05
0
5
27. m 0
rise
run
difference of y-coordinates
difference of x-coordinates
5 0
0 (1)
5
1
28. m 5
rise
run
difference of y-coordinates
difference of x-coordinates
2 (2)
8 3
0
11
29. m rise
run
difference of y-coordinates
difference of x-coordinates
16 87
82 65
71
17
71
17
rise
33. m run
difference of y-coordinates
difference of x-coordinates
0 10
10 (10)
10
0
32. m The slope is undefined.
34. Sample answer: A line with zero slope is a horizontal
line, and a line with undefined slope is a vertical line.
35. Let x the run.
rise
slope run
1
22
12
x
1 p x 12 p 22
0
rise
run
difference of y-coordinates
difference of x-coordinates
6 (6)
2 (2)
12
0
30. m The slope is undefined.
rise
run
difference of y-coordinates
difference of x-coordinates
6 (8)
2 (8)
2
6
1
3
31. m x 264
1 foot
冫 22 feet
264 inches 264 inches
12 in冫
ches
The length of ground the ramp covers is 22 feet.
400 0
0.1 0
400
0.1
36. a. Gradient 4000
The gradient between A and B is 4000 feet per mile.
500 400
0.2 0.1
100
0.1
b. Gradient 1000
The gradient between B and C is 1000 feet per mile.
500 0
0.2 0
500
0.2
c. Gradient 2500
The gradient between A and C is 2500 feet per mile.
37. a. No. Sample answer: First, find the slope of the road.
rise
63
3
m 7.5%
run
840
40
The road has a grade of 7.5% which is less than 8%,
so no warning sign should be posted.
––CONTINUED––
292
Pre-Algebra
Chapter 8 Solutions Key
LAHPA11FLSOL_c08.indd 292
Copyright © Holt McDougal
All rights reserved.
2/4/09 12:50:18 PM
Chapter 8 continued
37. ––CONTINUED––
39. ––CONTINUED––
b. Let x the rise.
rise
run
difference of y-coordinates
difference of x-coordinates
31
4 (1)
2
3
2
3
rise
R and S: m run
difference of y-coordinates
difference of x-coordinates
1 (1)
1 2
2
3
2
3
rise
Q and T: m run
difference of y-coordinates
difference of x-coordinates
3 (3)
4 5
6
9
2
3
b. Q and R: m rise
m run
x
9% 1000
x
0.09 1000
x
1000(0.09) 1000 p 1000
90 x
The road rises 90 feet.
3
rise
15
10
run
50
rise
30
2
Trail B: m 0.4
run
75
5
38. Trail A: m 0.3
Because 0.4 > 0.3, trail B is steeper. Therefore, the
instructor should take trail A.
39. Sample answer:
rise
run
difference of y-coordinates
difference of x-coordinates
0 (1)
2 (4)
1
2
rise
B and D: m run
difference of y-coordinates
difference of x-coordinates
20
2 (2)
2
4
1
2
rise
C and E: m run
difference of y-coordinates
difference of x-coordinates
31
40
2
4
1
2
a. A and B: m Conclusion: The slope does not depend on which two
different points are chosen.
––CONTINUED––
Conclusion: The slope does not depend on which two
different points are chosen.
40. Sample answer: Use the point P(x, y).
difference of y-coordinates
rise
m run
difference of x-coordinates
1y
1
9
1 x
Let y 2 and x 8.
1
1
12
1 8
9
9
1
So, the line through P(8, 2) and (1, 1) has a slope of 9.
8.4 Mixed Review (p. 425)
41.
x 7 5
x 7 7 5 7
x 12
Check:
x 7 5
12 7 ⱨ 5
5 5 ✓
Copyright © Holt McDougal
All rights reserved.
LAHPA11FLSOL_c08.indd 293
Pre-Algebra
Chapter 8 Solutions Key
293
2/4/09 12:50:19 PM
Chapter 8 continued
x 3 21
42.
50.
x 3 3 21 3
9x 2y 18
9x 2y 18
9x 2(0) 18
9(0) 2y 18
9x 18
2y 18
x2
y9
x 24
Check: x 3 21
24 3 ⱨ 21
The x-intercept is 2, and the y-intercept is 9.
21 21 ✓
y
9
(0, 9)
8
7
43. 3y 33
3y
33
3
3
6
5
4
y 11
Check:
3
2
1
3y 33
3(11) ⱨ 33
3 2
33 33 ✓
44.
51.
m
10
5
m
5 5(10)
5
(2, 0)
1
3 4 5 x
3x 4y 24
3x 4y 24
3x 4(0) 24
3(0) 4y 24
3x 24
4y 24
x 8
y 6
冢 冣
m 50
O
The x-intercept is 8, and the y-intercept is 6.
m
Check: 10
5
50
ⱨ 10
5
y
1
(8, 0)
8
6 5 4 3 2
O
x
2
3
4
5
10 10 ✓
45. 15 3 p 5
(0, 6)
48 2 p 2 p 2 p 2 p 3
7
The GCF of 15 and 48 is 3.
46. 64 2 p 2 p 2 p 2 p 2 p 2
8.4 Standardized Test Practice (p. 425)
56 2 p 2 p 2 p 7
rise
run
difference of y-coordinates
difference of x-coordinates
4 (14)
5 (1)
18
6
52. D; m The GCF of 64 and 56 is 23 8.
47. 105 3 p 5 p 7
125 5 p 5 p 5
The GCF of 105 and 125 is 5.
48. 121 11 p 11
132 2 p 2 p 3 p 11
The GCF of 121 and 132 is 11.
49. 2x y 2
2x y 2
2x 0 2
2(0) y 2
2x 2
y 2
x1
y 2
The x-intercept is 1, and the y-intercept is 2.
y
4
3
2
1
4 3 2
O
2
(1, 0)
3
rise
53. G; m run
difference of y-coordinates
difference of x-coordinates
40
20
4
2
2
1 2 3 4 x
(0, 2)
4
294
Pre-Algebra
Chapter 8 Solutions Key
LAHPA11FLSOL_c08.indd 294
Copyright © Holt McDougal
All rights reserved.
2/4/09 12:50:21 PM
Chapter 8 continued
Focus on Graphing
Lesson 8.5
Practice (p. 427)
8.5 Checkpoint (pp. 431–432)
1. Sample answer: Water is poured into the glass, then
someone drinks the water in four gulps, pausing between
gulps.
2. Sample answer: The swimmer climbs the diving board,
1. y x 1
y 1x 1
The line has a slope of 1 and a y-intercept of 1.
y
pauses, then leaps into the air and plunges into the water.
The swimmer’s descent through the air is slightly faster
than the descent through the water. After swimming at the
same elevation for a while, the swimmer rapidly surfaces.
3.
Distance traveled (miles)
1
1
(0, 1)
O
3 4 x
(1, 0)
2
3
4
16
12
2. 3x 2y 6
2y 3x 6
8
3
y 2x 3
4
0
0
4
8
12
16
Time (minutes)
3
y 2x (3)
20 x
3
The line has a slope of 2 and a y-intercept of 3.
y
100
Temperature (°C)
2
4 3 2
y
20
4.
4
3
y
4
3
90
2
1
80
4 3 2
(2, 0)
O
1
3 4 x
70
3
(0, 3)
2
60
0
0
10
20
30
40
Elapsed time (minutes)
50 x
Sample answer: The water cools at successively slower
rates over time.
3. y 4x
y 4x 0
The line has a slope of 4 and a y-intercept of 0.
Student Reference: Parallel, Perpendicular, and
Skew Lines
Checkpoint (p. 429)
1. Lines a and b are parallel.
y
4
3
(1, 4)
2
4
(0, 0)
4 3 2
O 1
2 3 4 x
2. Lines a and c are perpendicular.
3. Lines d and b are perpendicular.
4
4. Lines c and d are parallel.
5. Lines k and m are not skew because they lie in the
same plane and intersect.
6. Lines k and j are not skew because they intersect.
7. Lines j and m are skew because they do not lie in the
same plane and do not intersect.
^&(, AG
&
^ (, and EF
^&( are perpendicular to GE
^&(.
8. CE
^&( and BD
^&( are parallel to AC
&
^ (.
9. GE
4. y 3x
The slope of a parallel line is 3, and the slope of a
1
perpendicular line is 3.
5. y 4x 10
The slope of a parallel line is 4, and the slope of a
1
perpendicular line is 4.
^&( and ^JH
&( are skew to CD
^&(.
10. GE
Copyright © Holt McDougal
All rights reserved.
LAHPA11FLSOL_c08.indd 295
Pre-Algebra
Chapter 8 Solutions Key
295
2/4/09 12:50:23 PM
Chapter 8 continued
6. 2x 5y 15
6. y x
5y 2x 15
2
x
5
y
The slope of a parallel line is 1, and the slope of a
perpendicular line is 1.
3
2
The slope of a parallel line is 5, and the slope of a
5
perpendicular line is 2.
8.5 Guided Practice (p. 433)
7. y 6x 9
The slope of a parallel line is 6, and the slope of a
1
perpendicular line is 6.
8. 3x 2y 16
2y 3x 16
1. An equation of the form y mx b is written in
slope-intercept form.
3
2. Parallel. Sample answer: The lines y 7x 1 and
y 7x 3 both have a slope of 7 and different
y-intercepts. Because their slopes are equal and they
have different y-intercepts the lines are parallel.
y 2x 8
3
The slope of a parallel line is 2, and the slope of a
2
perpendicular line is 3.
9. (1) y 24 8x
3. y 2x
(2) The line has a slope of 8 and a y-intercept of 24.
y 2x 0
Scarf Knitting
The line has a slope of 2 and a y-intercept of 0.
y
Scarf length (in.)
4
3
(1, 2)
2
2
(0, 0)
4 3 2
2 3 4 x
1
2
3
4
4. y 3x 4
The line has a slope of 3 and a y-intercept of 4.
12. B
parallel to y 3x 2.
14. y 2x 3
(1, 1)
O
11. A
13. Sample answer: y 3x, y 3x 2, and y 3x 4 are
3
2
1
3 2
10. C
1
3
(3) It will take about 6 days to finish the scarf.
8.5 Practice and Problem Solving (pp. 433–435)
y
6
(0, 4)
y
72
64
56
48
40
32
24
(0, 24)
16
8
0
0 1 2 3 4 5 6 7 x
Day
1 2 3 4 5 x
The line has a slope of 2 and a y-intercept of 3.
2
y
5
5. x 2y 2
(0, 3)
2y x 2
1
2
2
1
1
y 2x 1
3 2
(1, 1)
O
1
2 3 4 5 x
2
3
1
y 2x (1)
1
The line has a slope of 2 and a y-intercept of 1.
y
4
3
1
15. y 4x 1
1
The line has a slope of 4 and a y-intercept of 1.
2
1
4 3 2
O
2
3
4
y
4
3
(2, 0)
4 x
1
2
(0, 1)
(4, 2)
(0, 1)
1
4
4 3 2
O
1 2 3 4 x
2
3
4
296
Pre-Algebra
Chapter 8 Solutions Key
LAHPA11FLSOL_c08.indd 296
Copyright © Holt McDougal
All rights reserved.
2/4/09 12:50:25 PM
Chapter 8 continued
16. y 2
20. Let x the number of minutes, and let y the distance
in feet.
y 0x (2)
The line has a slope of 0 and a y-intercept of 2.
Distance traveled Feet per minute p Number of minutes
y 10x
y
3
The line has a slope of 10 and a y-intercept of 0.
2
1
4 3 2
Robot Travel
O
240
(0, 2)
Distance (ft)
3
4
y
270
1 2 3 4 x
5
17. 3x y 1
y 3x 1
180
150
120
90
60
30
0
y 3x (1)
The line has a slope of 3 and a y-intercept of 1.
0 3 6 9 12 15 18 21 24 27 x
Time (min)
The robot could reach the end of the tunnel in about
21 minutes.
y
3
2
21. a. y 2000 250x
1
4 3 2
210
O 1
2 3 4 x
Y1=2000-250X
(0, 1)
3
3
4
5
(1, 4)
X=8
Y=0
18. 2x 3y 0
3y 2x
It takes the paramotorist 8 minutes to reach the ground.
b. The line has a slope of 250 and a y-intercept of 2000.
2
y 3x
y
2
x
3
The slope represents the rate at which the paramotorist
descends in feet per minute, and the y-intercept
represents the beginning height in feet.
0
2
The line has a slope of 3 and a y-intercept of 0.
22. y 8x 5
The slope of a parallel line is 8, and the slope of a
y
4
3
1
perpendicular line is 8.
(3, 2)
2
23. y x 9
2
(0, 0)
4 3 2
3
3
The slope of a parallel line is 1, and the slope of a
perpendicular line is 1.
4 x
2
3
4
24. y 7x 4
The slope of a parallel line is 7, and the slope of a
1
perpendicular line is 7.
19. 5x 2y 4
25. 4x 5y 30
2y 5x 4
y
5
x
2
5y 4x 30
2
4
The line has a slope of
y
5
2
(2, 7)
7
6
5
4
and a y-intercept of 2.
y 5x 6
4
The slope of a parallel line is 5, and the slope of a
5
perpendicular line is 4.
5
3
(0, 2)
4 3 2
O
2
1 2 3 4 x
Copyright © Holt McDougal
All rights reserved.
LAHPA11FLSOL_c08.indd 297
Pre-Algebra
Chapter 8 Solutions Key
297
2/4/09 12:50:28 PM
Chapter 8 continued
26. 11x 6y 18
31. a. Let x the number of days, and let y the
unharvested area of the larger field.
6y 11x 18
Unharvested
Total
Acres harvested Number
p
area
area
per day
of days
11
y 6 x 3
11
The slope of a parallel line is 6, and the slope of a
perpendicular line is
unharvested area of the smaller field.
x 3y 7
27.
Unharvested
Total
Acres harvested Number
p
area
area
per day
of days
x 7 3y
1
x
3
y 1000 50x
b. Let x the number of days, and let y the
6
.
11
7
3 y
y 600 50x
The slope of a parallel line is
perpendicular line is 3.
1
,
3
and the slope of a
rise
run
difference of y-coordinates
difference of x-coordinates
41
3
3
21
1
c. In part (a), the slope of the line is 50 and the
y-intercept is 1000. In part (b), the slope of the line
is 50 and the y-intercept is 600.
28. m 1
perpendicular line is 3.
rise
run
difference of y-coordinates
difference of x-coordinates
31
03
2
3
2
3
29. m 2
The slope of a parallel line is 3, and the slope of a
3
perpendicular line is 2.
rise
run
difference of y-coordinates
difference of x-coordinates
32
1 (3)
1
4
30. m The slope of a parallel line is
perpendicular line is 4.
298
1
,
4
and the slope of a
Pre-Algebra
Chapter 8 Solutions Key
LAHPA11FLSOL_c08.indd 298
Unharvested area (acres)
The slope of a parallel line is 3, and the slope of a
Corn Harvesting
y
(0, 1000)
1000
900
800
700
(0, 600)
600
500
400
300
200
y 1000 50x
100
y 600 50x
0
0 2 4 6 8 10 12 14 16 18 20 x
Time (days)
d. The graphs are parallel because both lines have the
same slope, 50, and different y-intercepts.
e. It takes 20 days to harvest the corn in the larger field.
It takes 12 days to harvest the corn in the smaller field.
32. a. Let x the number of miles, and let y the amount
of money.
Donor
Amount
per mile
Fixed
amount
Equation
Janette
None
$35
y 35
Ben
$2
$20
y 2x 20
Salil
$5
None
y 5x
Mary
$3
$15
y 3x 15
b. y 35 (2x 20) 5x (3x 15), or
y 10x 70.
c. The equation from part (b) has the greatest slope
because the slope is equal to the sum of the slopes in
part (a).
Sample answer: The slope represents how much
money is earned per mile. The equation from part
(b) is the sum of the slopes from parts (a). So, the
equation from part (b) has the greatest slope.
Copyright © Holt McDougal
All rights reserved.
2/4/09 12:50:30 PM
Chapter 8 continued
33. a. y mx b
y mx b
y m(0) b
y m(1) b
yb
ymb
(0, b) is a solution.
(1, m b) is a solution.
b. (m b) b m b b m
The difference of the y-coordinates is m.
101
The difference of the x-coordinates is 1.
difference of y-coordinates
rise
m
c. m m
run
1
difference of x-coordinates
So, the slope of y mx b is m.
37. 14c 33 10c 5
4c 33 5
4c 33 33 5 33
4c 28
4c
28
4
4
c 7
Check:
55 ✓
38. a p% p b 20% p 50 0.2 p 50 10
8.5 Mixed Review (p. 435)
34.
100 is 125% of 80.
40.
a p% p b
41.
56 p% p 140
45 0.75 p b
Check: 2(x 4) 16
2(12 4) ⱨ 16
16 16 ✓
35.
20 4(7 3z)
20 28 12z
20 28 12z
48 12z
48
12z
12
12
4z
Check: 20 4(7 3z)
20 ⱨ 4[7 3(4)]
20 20 ✓
36. 6 5a 13 8
5a 7 8
5a 7 7 8 7
5a 15
0.4 p%
60 b
40% p%
45 is 75% of 60.
56 is 40% of 140.
rise
42. m run
difference of y-coordinates
difference of x-coordinates
80
20
8
2
4
rise
run
difference of y-coordinates
difference of x-coordinates
1 5
41
6
3
43. m 2
5a
15
5
5
a 3
6 5a 13 8
6 5(3) 13 ⱨ 8
8 8 ✓
LAHPA11FLSOL_c08.indd 299
a p% p b
45 75% p b
2x
24
2
2
x 12
Copyright © Holt McDougal
All rights reserved.
10 is 20% of 50.
39. a p% p b 125% p 80 1.25 p 80 100
2(x 4) 16
2x 8 16
2x 8 8 16 8
2x 24
Check:
14c 33 10c 5
14(7) 33 10(7) ⱨ 5
rise
run
difference of y-coordinates
difference of x-coordinates
46
52
2
3
2
3
44. m Pre-Algebra
Chapter 8 Solutions Key
299
2/4/09 12:50:32 PM
Chapter 8 continued
rise
run
difference of y-coordinates
difference of x-coordinates
17 7
1 (3)
10
5
4
2
45. m Mid-Chapter Quiz (p. 438)
1.
y
6
5
2
1
4 3 2
46. D
y 500 25x
The line has a slope of 25 and a y-intercept of 500.
2
1
2
3
4
1 2 3 4 x
The relation is not a function because the input 2 is paired
with four outputs, 1, 2, 3, and 4.
47. Let x the number of weeks, and let y the remaining
Remaining
Total
Minutes used Number
p
calling time
minutes
per week
of weeks
O
Output
2
8.5 Standardized Test Practice (p. 435)
calling time.
(2, 4)
(2, 3)
(2, 2)
(2, 1)
4
3
Input
2.
y
Input
4
3
2
4
6
8
2
1
(4, 0)
O
(6, 0)
1 2 3 4 5 6 7 8 x
(2, 1)
Output
1
0
(8, 1)
Minutes remaining
Phone Card
y
500
450
400
350
300
250
200
150
100
50
0
The relation is a function because every input is paired
with exactly one output.
3. y x 7
0 2 4 6 8 10 12 14 16 18 20 x
Weeks
Focus on Graphing
Practice (p. 437)
1. The graph on the left represents direct variation. The
pressure from the water varies directly with the depth
of the dive. The constant of variation k is 0.1. It is the
slope of the graph and represents the rate of change in the
pressure of the water per meter of depth.
The graph on the right does not represent direct variation
because the line does not pass through the origin and the
ratios for the labeled points on the graph are not equal.
Cost (Dollars)
2. a.
x
2
1
0
1
2
y
9
8
7
6
5
y
7
6
5
4
3
2
1
x
1 2 3 4 5 6 7
O
The equation is a function.
4. x 5
y
4
3
y
50
2
40
O
30
2
3
4
1
1 2 3 4
6 7 x
20
10
0
The equation is not a function.
0
10
20
30
40
50 x
Perimeter of Frame (Inches)
The slope of the graph is 0.75, which represents the
cost per inch of the frame.
b. Answers may vary. A reasonable answer would be a
picutre that measures 7 inches by 7 inches.
300
Pre-Algebra
Chapter 8 Solutions Key
LAHPA11FLSOL_c08.indd 300
Copyright © Holt McDougal
All rights reserved.
2/4/09 12:50:34 PM
Chapter 8 continued
5. y 1
8. 4x y 8
4x y 8
4x 0 8
4(0) y 8
4x 8
y 8
y
4
3
2
x2
1
4 3 2
O
y 8
The x-intercept is 2, and the y-intercept is 8.
1 2 3 4 x
y
2
3
4 3 2
4
O
(2, 0)
1
3 4 x
2
3
4
The equation is a function.
5
6
6. x 4y 32
7
(0, 8)
8
4y x 32
1
y 4x 8
9.
x
8
4
0
4
8
y
10
9
8
7
6
y 2x 6
y 2x 6
0 2x 6
y 2(0) 6
2x 6
The x-intercept is 3, and the y-intercept is 6.
7
6
5
4
3
y
1
4 3 2
O
1
O
6
6x 3y 12
6x 3y 12
6x 3(0) 12
6(0) 3y 12
6x 12
3y 12
x2
10.
5x 2y 10
5x 2(0) 10
5(0) 2y 10
5x 10
2y 10
y4
x 2
6
y
6
5
(0, 4)
2
1
O
y5
The x-intercept is 2, and the y-intercept is 5.
y
3 2
(0, 6)
5x 2y 10
The x-intercept is 2, and the y-intercept is 4.
4
3
3 4 x
4
5
1 2 3 4 5 x
The equation is a function.
7.
(3, 0)
1 2
2
3
2
3 2
y 6
x3
y
3
2
(2, 0)
1 2
3 4 5 x
2
(0, 5)
(2, 0)
4 3
1
O
1
2
3
4 x
rise
run
11. m }
difference of y-coordinates
difference of x-coordinates
82
21
6
1
6
Copyright © Holt McDougal
All rights reserved.
LAHPA11FLSOL_c08.indd 301
Pre-Algebra
Chapter 8 Solutions Key
301
2/4/09 12:50:36 PM
Chapter 8 continued
rise
run
12. m }
Brain Game (p. 438)
difference of y-coordinates
difference of x-coordinates
44
40
0
4
y
(2, 4)
3
2
1
4 3 2
O
1
3 4 x
2
3
0
rise
run
13. m }
5 states had quarters issued each year.
difference of y-coordinates
difference of x-coordinates
2 10
1 (6)
8
7
8
7
rise
14. m }
run
difference of y-coordinates
difference of x-coordinates
62
1 (1)
4
0
The slope is undefined.
15. Let x the number of plays, and let y the total cost.
Total
Cost per Number
Registration
p
cost
play
of plays
fee
y 40x 50
The line has a slope of 40 and a y-intercept of 50.
Drama Festival
Total cost ($)
y
400
350
300
250
200
150
100
50
0
Lesson 8.6
8.6 Checkpoint (pp. 439–440)
1. y mx b
y 1x 5
yx5
4 6
0 (2)
10
2
2. m 5
b 4
y 5x (4)
y 5x 4
3. A graph. Sample answer: A table shows discrete input
and output values, while a graph can show those values
and intermediate values. A graph also makes it easier
to determine whether or not the points lie on a
nonvertical line, whereas you cannot tell immediately if a
function is linear when looking at a table of values.
8.6 Guided Practice (p. 442)
1. The line that lies as close as possible to the data points in
a scatter plot is called the best-fitting line.
2. Sample answer: First, find the slope using the two points.
6
93
m 3
0 (2) 2
Find the y-intercept. The line crosses the y-axis at (0, 9),
so b 9.
Write an equation of the form y mx b.
y 3x 9
0 1 2 3 4 5 6 7 8 9 x
Number of Plays
98
10
1
1
3. m 1
b8
y mx b
y 1x 8
yx8
1 13
0 (2)
12
2
4. m 6
b1
y mx b
y 6x 1
302
Pre-Algebra
Chapter 8 Solutions Key
LAHPA11FLSOL_c08.indd 302
Copyright © Holt McDougal
All rights reserved.
2/4/09 12:50:38 PM
Chapter 8 continued
3 (5)
30
0 (2)
30
2
3
5. m b 5
b 2
y mx b
y mx b
2
y x (5)
3
2
y x (2)
3
2
y x 5
3
2
y x 2
3
6. The slope of the given line is 2, so the slope of the
1
perpendicular line is 2. The y-intercept is 7.
1
y 2x (7)
Butter Clams
Length (mm)
y
90
60
50
40
30
20
10
0
16 (6)
80
5
4
b 6
0 10 20 30 40 50 60 70 80 90 x
Width (mm)
y mx b
5
y x (6)
4
5
y x 6
4
(3) y 1.26x 1.4
y 1.26(85) 1.4
y ≈ 109
The length of the butter clam is about
109 millimeters.
8.6 Practice and Problem Solving (pp. 442–444)
9. y mx b
y 4x 10
11. y mx b
y 13x (8)
y 1x (20)
y 13x 8
y x 20
y 3x 1
10
8
16. m y 1.26x 1.4
y mx b
6
3
y 2x 9
The line intersects the y-axis at 1.4.
b1
15 9
30
15. m 2
y mx b
77 14
63
m 1.26
60 10
50
41 3
12. m 3
10 1
b3
b9
80
70
(2) Sample answer: Using (10, 14) and (60, 77):
10. y mx b
4
2
y 2x 3
7. (1) Sample answer:
y 3x 5
3 (1)
02
14. m 2
y mx b
1
y 2x 7
8. y mx b
2
3
13. m 11 (11)
0 (2)
0
2
17. m 0
b 11
y mx b
y 0x (11)
y 11
18. The slope of the given line is 2, so the slope of the
parallel line is also 2. The y-intercept is 4.
y 2x 4
19. The slope of the given line is 1, so the slope of the
parallel line is also 1. The y-intercept is 7.
y 1x 7
y x 7
20. The slope of the given line is 8, so the slope of the
parallel line is also 8. The y-intercept is 2.
y 8x (2)
y 8x 2
21. The slope of the given line is 3, so the slope of the
1
perpendicular line is 3. The y-intercept is 6.
1
y 3x 6
22. The slope of the given line is 1, so the slope of the
perpendicular line is 1. The y-intercept is 5.
y 1x (5)
y x 5
Copyright © Holt McDougal
All rights reserved.
LAHPA11FLSOL_c08.indd 303
Pre-Algebra
Chapter 8 Solutions Key
303
2/4/09 12:50:40 PM
Chapter 8 continued
1
23. The slope of the given line is 4, so the slope of the
26. ––CONTINUED––
b. Sample answer: Using (20, 9.5) and (60, 5):
perpendicular line is 4. The y-intercept is 1.
y 4x 1
24.
4.5
5 9.5
m 0.1125
40
60 20
y
7
6
5
(2, 7)
The line intersects the y-axis at 11.75.
y 0.1125x 11.75
4
3
(1, 4)
0 0.1125x 11.75
c.
0.1125x 11.75
2
1
4 3 2
1
(1, 2)
(2, 5)
(0, 1)
2
3
x ≈ 104
4 x
1912 104 2016
2
The glaciers will disappear in about 2016.
3
4
5
27.
The y-intercept is 1.
y 3x
4
k
(6, 0)
1 2 3 4
6 7 8 x
3 k
(4, 1)
(2, 2)
(0, 3)
10 1
m 86 2
The y-intercept is 3.
y mx b
1
y x (3)
2
1
y x 3
2
26. a. (0, 12.1), (41, 6.7), (64, 4.2), (77, 3.3), (88, 2.2)
Kilimanjaro Glaciers
y
14
12
10
8
6
4
2
0
sales. Let y the total earnings.
Lisa: Total
Percent
Annual
p
Salary
earnings
commission sales
y 0.02x 18,000
John: Total
Percent
Annual
p
earnings
commission sales
y 0.06x
For Lisa, annual sales and annual earnings do not show
direct variation because of the constant term. For John,
annual sales and annual earnings do show direct variation
with k 0.06.
32. a.
Spring Stretching
y
225
(200, 200)
200
175
(150, 170)
150
(100, 140)
125
100
(50, 110)
75
(0, 80)
50
25
0
0 10 20 30 40 50 60 70 80 90 x
Years since 1912
––CONTINUED––
Pre-Algebra
Chapter 8 Solutions Key
LAHPA11FLSOL_c08.indd 304
4
y 3x
31. Lisa: no; John: yes. Sample answer: Let x the annual
Length (mm)
(8, 1)
1
Area (km2)
16 k(12)
1
2
304
y kx
30.
y 2x
3
4
5
y 7x
y kx
1
2
y
2
7 k
4 k(8)
y 3x 1
O
21 k(3)
3k
29.
y mx b
y kx
28.
15 k5
71 6
m 3
20 2
25.
y kx
0
50
100 150 200
Mass (g)
250 x
The points lie on a nonvertical line, so the table
represents a linear function.
––CONTINUED––
Copyright © Holt McDougal
All rights reserved.
2/4/09 12:50:42 PM
Chapter 8 continued
32. ––CONTINUED––
8.6 Mixed Review (p. 444)
170 110
3
60
b. m 150 50
100 5
The y-intercept is 80.
35.
y mx b
3
y x 80
5
33. a.
8x 5 5x 7
8x 5 5x 5x 7 5x
3x 5 7
3x 5 5 7 5
3x 12
3x 12
3
3
Winning time (min)
Boston Marathon
y
160
150
140
130
120
110
100
0
0
20
40
60
80
Years since 1900
100 x
b. Sample answer: Using (0, 160) and (90, 130):
130 160 30
1
m 90 0
90
3
The line intersects the y-axis at 160.
1
y 3x 160
1
c. y 3 (110) 160
y ≈ 123
The men’s winning time in 2010 will be about
123 minutes.
d. No. Sample answer: The equation predicts a winning
time of 0 minutes eventually, which is impossible. I
would expect the winning times eventually to level off
and decrease very little, if any.
34. First, find the slope.
5 (1) 6 3
m 62
4 2
Substitute m into the equation y mx b.
3
y x b
2
x4
Check: 8x 5 5x 7
8(4) 5 ⱨ 5(4) 7
27 27 ✓
36.
7y 4 y 22
7y 4 y y 22 y
6y 4 22
6y 4 4 22 4
6y 18
6y
18
6
6
y 3
Check:
7y 4 y 22
7(3) 4 ⱨ (3) 22
25 25 ✓
37.
4(m 4) 2m
4m 16 2m
4m 16 4m 2m 4m
16 2m
16 2m
2
2
8m
Check: 4(m 4) 2m
4(8 4) ⱨ 2(8)
16 16 ✓
38. 6(1 n) 6n 1
6 6n 6n 1
To find the y-intercept, substitute (2, 1) into the
equation and solve for b.
3
1 (2) b
2
1 3 b
4 b
3
So, the y-intercept is 4. The equation is y x (4)
2
3
x
or y 4.
2
61
No solution
3
7
40. 8 0.375 37.5%
5
42. 5 1.8 180%
39. 1
0.7 70%
0
9
41. 2 2.5 250%
43. y 3x 2
The line has a slope of 3 and a y-intercept of 2.
y
3
2
(1, 1)
1
3 2
O
3
3
4
5 x
(0, 2)
1
5
Copyright © Holt McDougal
All rights reserved.
LAHPA11FLSOL_c08.indd 305
Pre-Algebra
Chapter 8 Solutions Key
305
2/4/09 12:50:44 PM
Chapter 8 continued
44. y x 5
8.6 Technology Activity (p. 445)
The line has a slope of 1 and a y-intercept of 5.
7
6
y 9.8929(13) 108.25
1
y 236.8577
(0, 5)
1
4
3
2
In 2005, there will be about 237,000 female physicians in
the United States.
2. The best-fitting line for the data is y 8.93x 139.
(1, 4)
1
2
1. y 9.8929x 108.25
y
1
O
2
3
4
5
Focus on Functions (p. 447)
6 x
1.
y
4
3
2
1
45. 3x 2y 0
2y 3x
3
y 2x
4 3 2
The line has a slope of
3
2
y
2.
2
O
3
y
6
5
4
3
2
1
4 x
3
2
3
4
(2, 3)
3 2
46. x 2y 2
1
3.
4
5 x
y
4
3
2
1
The line has a slope of 2 and a y-intercept of 1.
y
1
4
4 3 2
(2, 2)
(0, 1)
1
1
2
3
4
5 x
2
3
4
1
O
2
3
4 x
2
3
4
2
O
3
The function is continuous. The range is y ≤ 6.
1
y 2x 1
2
2
2
2y x 2
3
4 x
The function is discrete. The range is 1, 1, 3, 5.
(0, 0)
4 3 2
3
2
3
4
and a y-intercept of 0.
4
3
2
2
O
The function is continuous. The range is y ≤ 2
4.
y
15
8.6 Standardized Test Practice (p. 444)
08
20
8
2
47. D; m 4
b8
y mx b
y 4x 8
5
23
21
25
1
3
x
215
The function is discrete. The range is 16, 8, 0, 8, 16.
48. F; The slope of the given line is 5, so the slope of the
parallel line is also 5. The y-intercept is 1.
y mx b
y 5x (1)
y 5x 1
306
Pre-Algebra
Chapter 8 Solutions Key
LAHPA11FLSOL_c08.indd 306
Copyright © Holt McDougal
All rights reserved.
2/4/09 12:50:46 PM
Chapter 8 continued
5. Let x represent the number of dogs that you wash. Let y
represent the profit in dollars. The cost of supplies is $25,
and each dog you wash brings in $6, so the equation for
the profit is given by y 25 6x. You cannot wash
part of a dog, so the domain consists of the whole numbers
0, 1, 2, 3, .... So the function is discrete.
3. g(x) 4x 5
19 4x 5
24 4x
6x
When g(x) 19, x 6.
y 25 6x
4. f(x) 2x 4
95 25 6x
y 2x 4
95 25 6x
The y-intercept is 4. The slope is 2.
120 6x
y
2
20 x
So you need to wash 20 dogs to have a profit of $95.
1
3 2
6. Let t represent the number of years since the tree is
measured to be 11 feet tall. Let h represent the height of
the tree in feet. The current height of the tree is 11 feet
tall, and each year the tree grows at the rate of 0.75 foot
per year, so the equation for the height is given by
h 11 0.75t. Time is continuous, so the domain is the
positive unit of time after the tree is measured. So the
function is continuous.
h 11 0.75x
23 11 0.75x
23 11 0.75x
O
3
represent the total weight of the bucket with the water in
pounds. The bucket weighs 1 pound when it is empty, and
1 quart of water weights about 2 pounds, so the equation
for the total weight is given by W 1 2V. You can
have a fraction of a quart of water in the bucket. So the
function is continuous.
W 1 2V
3
5. g(x) 2x 3
3
y 2x 3
3
The y-intercept is 3. The slope is 2.
y
5
4
2
3 2
O (2, 0)
4
y 1
The y-intercept is 1. The slope is 0.
y
4
3
2
1
4 3 2
O
2
3
4
1 2 3 4 x
(0, 1)
7. (0, 1), (2, 9)
g(2) 4(2) 5 3
91
8
m 4
20
2
When x 2, g(x) 3.
b1
g(x) 4x 5
g(10) 4(10) 5 45
Copyright © Holt McDougal
All rights reserved.
5 x
6. h(x) 1
Lesson 8.7
LAHPA11FLSOL_c08.indd 307
3
2
3
So the bucket with 4 quarts of water weighs 9 pounds.
2.
3
1
8 2V
1. g(x) 4x 5
2
(0, 3)
9 1 2V
8.7 Checkpoint (pp. 448–449)
1
6
9 1 2V
4V
2
(0, 4)
So the tree will be 23 feet tall in 16 years.
7. Let V represent the volume of water in quarts. Let W
2 3 4 5 x
(1, 2)
2
12 0.75x
16 x
1
f(x) mx b
f(x) 4x 1
Pre-Algebra
Chapter 8 Solutions Key
307
2/4/09 12:50:49 PM
Chapter 8 continued
8. (0, 7), (6, 5)
6. f(x) x 3
y x 3
5 (7)
12
m 2
60
6
The y-intercept is 3. The slope is 1.
b 7
y
5
4
f (x) mx b
f (x) 2x (7)
1
(0, 3)
1
2
f (x) 2x 7
1
9. (6, 16), (0, 5)
3 2
5 16
21
7
m 0 (6)
6
2
b 5
(1, 2)
O
1
2
3
4
5 x
7. g(x) 3x 5
y 3x 5
g(x) mx b
The y-intercept is 5. The slope is 3.
7
g(x) x (5)
2
7
g(x) x 5
2
y
2
1
3 2
O
1
10. (7, 3), (0, 3)
33
0
m 0
0 (7)
7
(0, 5)
2
3
4
5 x
(1, 2)
2
3
4
3
1
b3
r(x) mx b
8. h(x) 2x
r(x) 0x 3
y 2x
r(x) 3
The y-intercept is 0. The slope is 2.
8.7 Guided Practice (p. 450)
y
4
3
2
y 4x 3
1.
f (x) 4x 3
(0, 0)
2. Sample answer: The given values of f(x) mean that the
4 3 2
graph of f passes through (2, 5) and (6, 1).
Now use the definition of slope.
difference of y-coordinates
m difference of x-coordinates
1 5
62
6
4
3
2
So, the slope of f is
f (3) 7(3) 4 25
5. f (x) 7x 4
67 7x 4
63 7x
9x
When f(x) 67, x 9.
308
Pre-Algebra
Chapter 8 Solutions Key
LAHPA11FLSOL_c08.indd 308
3
4 x
b8
f(x) mx b
f(x) 1x 8
f(x) x 8
10. Let t the number of years since 1985. Let f(t) the
monthly cost of basic cable TV.
Monthly
Increase Number
Cost in
p
cost
per year of years
1985
f(t) 1.35t 9.73
f (8) 7(8) 4 52
When x 8, f(x) 52.
2
8 12
4
m 1
0 (4)
4
3
2.
4. f (x) 7x 4
O 1
9. (4, 12), (0, 8)
f (x) 7x 4
3.
(1, 2)
2
8.7 Practice and Problem Solving (pp. 451–452)
11.
f (x) 3x 1
f(1) 3(1) 1 4
When x 1, f (x) 4.
12. g(x) 10x 4
g(5) 10(5) 4 46
When x 5, g(x) 46.
Copyright © Holt McDougal
All rights reserved.
2/4/09 12:50:51 PM
Chapter 8 continued
13. f(x) 3x 1
22. ––CONTINUED––
17 3x 1
y
7
18 3x
6
6x
(0, 5)
3
5
4
When f(x) 17, x 6.
3
2
14. g(x) 10x 4
2
(3, 3)
1
31 10x 4
O
x
1
2
3
4
5
6
7
35 10x
3.5 x
23. The slope of the given line is 8, so the slope of the
When g(x) 31, x 3.5.
parallel line is also 8. The y-intercept is 0.
f (x) 3x 1
15.
g(x) mx b
f (20) 3(20) 1 61
g(x) 8x 0
16. f (x) 3x 1
g(x) 8x
f(4) 3(4) 1 11
24. (0, 4), (1, 7)
g(x) 10x 4
g(3) 10(3) 4 34
74
3
m 3
10
1
f (4) g(3) 11 (34) 45
b4
17. C
18. A
19. B
y 2x
25. (2, 10), (0, 0)
The y-intercept is 0. The slope is 2.
y
4
g(x) mx b
g(x) 5x 0
1
4 3 2
O
2 3 4 x
g(x) 5x
(1, 2)
2
3
4
26. (0, 13), (3, 1)
1 13
12
m 4
30
3
21. g(x) 4x 4
b 13
y 4x 4
The y-intercept is 4. The slope is 4.
y
2
1
3 2
h(x) 4x 13
1 (7) 6
2
m 0 (9)
9
3
(1, 0)
2
3
4
5 x
b 1
4
3
(0, 4)
h(x) mx b
27. (9, 7), (0, 1)
O
2
0 10
10
m 5
0 (2)
2
b0
3
2
(0, 0)
f(x) mx b
f(x) 3x 4
20. f (x) 2x
r(x) mx b
1
2
r(x) x (1)
3
2
r(x) x 1
3
2
22. h(x) 3x 5
2
y 3x 5
2
The y-intercept is 5. The slope is 3.
––CONTINUED––
Copyright © Holt McDougal
All rights reserved.
LAHPA11FLSOL_c08.indd 309
Pre-Algebra
Chapter 8 Solutions Key
309
2/4/09 12:50:53 PM
Chapter 8 continued
28. a. m(b) 236b 513
m(5) 236(5) 513 667
31. ––CONTINUED––
A(n) n2 n
d.
A(50) (50)2 50 2550
The mass of the squid is about 667 grams.
P(n) 4n 2
b. m(b) 236b 513
1100 236b 513
P(50) 4(50) 2 202
1613 236b
The area is 2550 square units, and the perimeter is
202 units.
6.8 ≈ b
The lower beak of the arrow squid is about
6.8 millimeters long.
Fixed
Cost per
Number of
p
costs
costs
birdhouse birdhouses
c(x) 10x 3000
29. a. Total
b.
Price of
Number of
p
birdhouse birdhouses
i(x) 50x
Income c. p(x) i(x) c(x)
33. 2n7 p 5n4 2 p 5 p n7 p n4 2 p 5 p n7 4 10n11
a1 2
a
34. a12 8 a4
8
30c 9 2
30c 9
38. 99% 100
Your profit is $1000.
p(x) 40x 3000
0 40x 3000
40x 3000
x 75
You will break even when you make and sell
75 birdhouses.
30. a. s(d ) 0.117d 1.68
y 0.117x 1.68
Y1=-.117X+1.68
5c 7
2
40
100
50x 10x 3000
p(x) 40x 3000
5
冫
30c 7
35. 2 冫
12
12
2
12 c
36. 40% p(100) 40(100) 3000 1000
e.
32. x 3 p x 5 x 3 5 x 8
50x (10x 3000)
40x 3000
d.
8.7 Mixed Review (p. 452)
64
2
5
16
37. 64% 100
25
99
150
3
39. 150% 100
2
40. The slope of the given line is 6, so the slope of the
1
perpendicular line is 6. The y-intercept is 4.
y mx b
1
y 6x (4)
1
y 6x 4
5
41. The slope of the given line is 9, so the slope of the
9
perpendicular line is 5. The y-intercept is 3.
y mx b
9
y 5x 3
8.7 Standardized Test Practice (p. 452)
42. D;
f(x) 7x 11
f (4) 7(4) 11 17
X=9
Y=.627
b. The speed of the current decreases as you go deeper
below the river’s surface.
c. s(d ) 0.117d 1.68
4 28
24
m 8
0 (3)
3
44. w(p) 0.878p 4764
Find w(p) when p 271,750.
s(9) 0.117(9) 1.68 0.627
w(271,750) 0.878(271,750) 4764 233,832.5
The speed of the current is 0.627 foot per second.
About 234,000 tons of solid waste was disposed of in
Marion County during 1998.
31. a. The dimensions of the nth rectangle are (n 1) by n.
b.
43. F; (3, 28), (0, 4)
A lw
A(n) (n 1)n n2 n
c.
P 2l 2w
P(n) 2(n 1) 2n 2n 2 2n 4n 2
––CONTINUED––
310
Pre-Algebra
Chapter 8 Solutions Key
LAHPA11FLSOL_c08.indd 310
Copyright © Holt McDougal
All rights reserved.
2/4/09 12:50:55 PM
Chapter 8 continued
3. 3x y 1
Lesson 8.8
y 3x 4
y 3x 1
8.8 Concept Activity (p. 453)
5
4
Draw Conclusions
1. The ordered pair represented by the student with both
hands raised satisfies both equations, so it is the solution
to the linear system.
y 3x 4
4 3 2
2. right hand raised: (0, 0), (2, 1), (4, 2)
y 3x 1
1
1 2 3 4 x
O
left hand raised: (0, 0), (1, 1), (2, 2), (3, 3), (4, 4)
both hands raised: (0, 0)
3. right hand raised: (0, 2), (2, 1), (4, 0)
left hand raised: (1, 0), (2, 1), (3, 2), (4, 3)
both hands raised: (2, 1)
4. right hand raised: (0, 1), (1, 2), (2, 3), (3, 4)
left hand raised: (0, 3), (1, 3), (2, 3), (3, 3), (4, 3)
both hands raised: (2, 3)
5. right hand raised: (0, 3), (1, 2), (2, 1), (3, 0)
left hand raised: (0, 1), (1, 1), (2, 1), (3, 1), (4, 1)
both hands raised: (2, 1)
The system has no solution.
4. One. Sample answer: If two lines in a plane are not
parallel (and are not the same line), they must intersect
in one point. Two lines in a plane with different slopes
are not parallel, so they must intersect in one point. In
the drawing, lines p and q are parallel and will never
intersect. Line r has a different slope from either p or q,
and will clearly intersect each in a single point.
y
p
6. Let y represent the amount of money saved in dollars. Let
x represent time in weeks. Then the linear system is as
follows:
Ashlyn: y 2x
Caleb: y 4 x
right hand raised: (0, 0), (1, 2), (2, 4), (3, 6), (4, 8)
left hand raised: (0, 4), (1, 5), (2, 6), (3, 7), (4, 8)
both hands raised: (4, 8)
So in 4 weeks they will have the same amount of money
saved.
yx2
y
6
y 4x 2
5
4
3
2
4 3
O
x
r
8.8 Guided Practice (p. 456)
1. A solution of a system of linear equations in two
variables is an ordered pair that is a solution of each
equation in the system.
2. If the graphs of the two equations in a system are parallel
8.8 Checkpoint (p. 455)
1. y 4x 2
q
lines, the linear system has no solution.
3. y 3x 8
y 2x 5
y
6
4
2
yx2
8 6 4
(0, 2)
1
4 6 8 x
4
1 2 3 4 x
y 2x 5
The solution is (0, 2).
2. x y 3
(3, 1)
O
4x 4y 12
y x 3
4y 4x 12
yx3
yx3
y 3x 8
The solution is (3, 1).
4. x y 3
x y 5
y x 3
y x 5
yx5
y
6
5
4
3
2
O
3
2
1
1 x
2
The system has infinitely many solutions.
Copyright © Holt McDougal
All rights reserved.
LAHPA11FLSOL_c08.indd 311
6
5
(1, 4)
2
1
yx3
7 6 5
xy3
y
4 3 2
x y 5
O
1 2 x
2
The solution is (1, 4).
Pre-Algebra
Chapter 8 Solutions Key
311
2/4/09 12:50:56 PM
Chapter 8 continued
5. y 4x 1
y 5 4x
13. y 3x 2
y 4x 5
y
y
5
yx2
2
1
y 5 4x
2
O
4
5
1
x
5
2 3 4
(1, 1)
2
y 4x 1
4 3 2
yx2
y 3x 2
1 2 3 4 x
O
The solution is (1, 1).
14. y 2x 1
The system has no solution.
6. Let x the types of court shoes, and let y the types of
y 4x 5
y
6
5
4
running shoes.
Types of
Types of
Total
court shoes
running shoes types
x y 120
y 2x 1
3
(2, 3)
2
1
y x 120
2
O
2 3 4
5
6 x
y 4x 5
Types of running shoes 2 p Types of court shoes
y 2x
The solution is (2, 3).
15. 2x 4y 8
3x 6y 12
4y 2x 8
y
Intersection
X=40
Y=80
1
2x
6y 3x 12
1
2
y 2x 2
y
4
The solution is (40, 80).
3
So, the store manager should display 40 types of court
shoes and 80 types of running shoes.
1
8.8 Practice and Problem Solving (pp. 457–458)
3x 2y 4
7.
2x y 2
3(0) 2(2) ⱨ 4
O
x
1 2 3 4
2
3
4
2(0) (2) ⱨ 2
44 ✓
2 2 ✗
The system has infinitely many solutions.
16. 2x y 8
(0, 2) is not a solution.
8. y 5x 22
2 ⱨ 5(4) 22
y 8x 30
2 ⱨ 8(4) 30
22 ✓
22 ✓
(4, 2) is a solution.
9.
3 2
y 12 x 2
x y 4
y 2x 8
x y 4
3
2
1
(4, 0)
x 4y 16
24 4(10) ⱨ 16
7 6 5
16 16 ✓
2x 6y 12
2(24) 6(10) ⱨ 12
yx4
2
2x y 8
O
1 x
2
3
4
The solution is (4, 0).
12 12 ✓
(24, 10) is a solution.
10. The solution is (2, 2).
11. The solution is (0, 3).
12. The solution is (2, 1).
312
Pre-Algebra
Chapter 8 Solutions Key
LAHPA11FLSOL_c08.indd 312
Copyright © Holt McDougal
All rights reserved.
2/4/09 12:50:59 PM
Chapter 8 continued
17. y 5x 3
y 5x 2
21. 4x y 5
3x 5y 25
y 4x 5
4
3
5y 3x 25
3
y 5y 5
2
1
y
4 3 2
1 2 3 4 x
(0, 5)
y 5x 2
y 5x 3
4
3
2
4
3x 5y 25
1
The system has no solution.
18. x y 7
O
yx3
4x y 5
y x 7
The solution is (0, 5).
22. Let x the number of pairs of skates, and let y the
yx3
2
1
7
5
1 2 3 4 5 6 7 8
2
number of bicycles.
Pairs of skates Number of bicycles Total rentals
1 x
O
x y 25
(5, 2) 2
y x 25
3
x y 7
4
5
Rent
Number
Rent per
Total
Pairs of
pair of p
per
p of
income
skates
bicycle bicycles
skates
The solution is (5, 2).
19. x 3y 6
15x 20y 450
2x 3y 3
3y x 6
20y 15x 450
3y 2x 3
1
3
y 4x 22.5
2
y 3x 2
y 3x 1
y
4
3
2x 3y 3
(3, 1)
Intersection
X=10
Y=15
1
6 5 4 3 2
1 x
2
3
4
x 3y 6
The solution is (10, 15).
The owner rented 10 pairs of skates and 15 bicycles.
23. Let x the number of newspaper ads, and let y the
The solution is (3, 1).
20. 3x 2y 8
4y 16 6x
2y 3x 8
3
y
3
2x
y
6
2
O
Newspaper ads Radio ads Total ads
y 4 2x
y 32x 4
4
3
2
1
number of radio ads.
y 32 x 4
x y 50
y x 50
4
Cost of
Number of
p
newspaper ad newspaper ads
Cost of
Number of
Total
p
radio ad radio ads
budget
600x 300y 24,000
300y 600x 24,000
1
2
4 5
6 x
y 2x 80
2
––CONTINUED––
The system has infinitely many solutions.
Copyright © Holt McDougal
All rights reserved.
LAHPA11FLSOL_c08.indd 313
Pre-Algebra
Chapter 8 Solutions Key
313
2/4/09 12:51:01 PM
Chapter 8 continued
23. ––CONTINUED––
25. ––CONTINUED––
c. Writing the equation in one variable based on the
verbal model suggested gives the following:
0.15x 100 0.03x 400
0.15x 0.03x 400 100
Intersection
X=30
Y=20
0.12x 300
x 2500
The solution is (30, 20).
You should run 30 newspaper ads and 20 radio ads
each month.
24. 2x y 4
y 2x 4
y 2x 4
2x 3y 12
3y 2x 12
d. The method used in (c) gives a concise algebraic
expression when the total cost of printing with both
printers is equal as the verbal model suggests. The
graphing method gives the same solution, but also
allows a visual representation of costs at points when
they are not equal to revenue. This is useful if you
want to decide which printer is more cost effective
given the number of pages you are expecting to print.
26. a. y 3x 2
2
y 3x 4
y mx b
10x 3y 12
For there to be one solution, the lines should have
different slopes.
3y 10x 12
Sample answer: Let m 5 and b 6.
10
y 3 x 4
y 5x 6
y
10
(3, 6)
2x 3y 12
12
8
y
8
6
5
4
3
2x y 4
(3, 2)
2
4
4
2
1
12 x
4 (0, 4)
10x 3y 12
The triangle’s vertices are (3, 2), (3, 6), and (0, 4).
25. a. Let x the number of pages printed, and let y the
total cost.
Cost of
Cost per Pages
Inkjet: Total
p
printer
cost
page
printed
y 0.15x 100
Cost of
Cost per Pages
Laser: Total
p
printer
cost
page
printed
y 0.03x 400
y 3x 2
2
O
(1, 1)
1 2
2
3
4
5
6 x
y 5x 6
b. y 3x 2
y mx b
For there to be no solution, the lines should be parallel,
which means that they must have the same slope but
not be the same line.
Sample answer: Let m 3 and b 1.
y 3x 1
y
4
3
b.
2
1
4 3 2
Intersection
X=2500
Y=475
The solution is (2500, 475).
After 2500 pages, the total cost of the printers
are equal.
y 3x 1
1 2
3
4 x
y 3x 2
––CONTINUED––
––CONTINUED––
314
Pre-Algebra
Chapter 8 Solutions Key
LAHPA11FLSOL_c08.indd 314
Copyright © Holt McDougal
All rights reserved.
2/4/09 12:51:03 PM
Chapter 8 continued
26. ––CONTINUED––
31.
c. y 3x 2
y mx b
n
< 6
2
n
2 p < 2 p 6
2
For there to be infinitely many solutions, the lines
must be the same.
n < 12
Sample answer: y 3x 2
y
3
y 3x 2
2
1
3 2
O
1 2
3
4
5 x
2
3
0
3
6
9
12
15
32. 1200 1.2 103
33. 309,000 3.09 105
34. 0.0005 5 104
35. 0.00000748 7.48 106
36. (0, 8), (3, 10)
10 8
2
m 30
3
b8
27. a. Let l the length, and let w the width of the pool.
A lw
f(x) mx b
450 lw
2
f(x) x 8
3
450
l
w
450
l w
37. (4, 7), (0, 27)
27 (7) 20
m 5
0 (4)
4
b 27
l 2w
y mx b
b. The ordered pair (15, 30) satisfies both equations. The
h(x) 5x (27)
length of the pool should be 30 feet, and the width of
the pool should be 15 feet.
8.8 Mixed Review (p. 458)
x4>9
28.
h(x) 5x 27
8.8 Standardized Test Practice (p. 458)
38. C; y 2x 16
x44>94
x>5
0
29.
1
2
3
4
5
y≤7
4
66 ✓
66 ✓
x 3y 12
39. F;
y55≤25
3
y x 1
6 ⱨ (5) 1
(5, 6) is a solution.
6
y5≤2
2
6 ⱨ 2(5) 16
3x 9y 36
3 3(2) ⱨ 12
3(3) 9(2) ⱨ 36
9 12
27 36
(3, 2) is not a solution.
5
6
7
8
30. 3t ≥ 12
1. According to the table shown above, when x 5, that is
3t 12
≤ 3 3
after 5 months, they will each have 275 songs.
2.
t ≤ 4
6 5 4 3 2 1
8.8 Technology Activity (p. 459)
8
0
9
9
8
(4, 1)
Copyright © Holt McDougal
All rights reserved.
LAHPA11FLSOL_c08.indd 315
Pre-Algebra
Chapter 8 Solutions Key
315
2/4/09 12:51:05 PM
Chapter 8 continued
3. y < 3
3.
8
9
9
Graph y 3 using a dashed line.
Test (0, 0).
y<3
0<3 ✓
8
Shade the half-plane that contains (0, 0).
y
(6, 22)
5
4
4.
8
9
9
y<3
2
4 3 2
O
1
8
3
4 x
fluid ounces of grapefruit juice.
Lesson 8.9
8.9 Checkpoint (pp. 461–462)
1. x 2y > 6
Vitamin
C in
orange
juice
Graph x 2y 6 using a dashed line.
Fluid
Vitamin C
ounces
p
in
p of
grapefruit
orange
juice
juice
Graph 15x 12y 60 using a solid line.
x 2y > 6
0 2(0) ?
>6
Test (0, 0).
15x 12y ≥ 60
15(0) 12(0) ?
≥ 60
0 >/ 6
Shade the half-plane that does not contain (0, 0).
0 ≥/ 60
y
Shade the half-plane that does not contain (0, 0).
x 2y > 6
Vitamin C Sources
1
Grapefruit juice (fl oz)
2
x
1
2
3
4
5
6
2
3
2. x ≥ 1
Graph x 1 using a solid line.
Test (0, 0).
15x 12y ≥ 60
1
0
0 1 2 3 4 5 6 7 x
Orange juice (fl oz)
1. The graph of a linear inequality in two variables is called
0 ≥ 1 ✓
Shade the half-plane that contains (0, 0).
y
a half-plane.
2. Sample answer: When graphing a linear inequality in
two variables, test a point in one of the half-planes to
determine whether it is a solution. If the test point is a
solution, shade the half-plane that contains the point. If
not, shade the other half-plane.
4
3
2
x ≥ 1
1
4 3 2
y
7
6
5
4
3
2
8.9 Guided Practice (p. 463)
x ≥ 1
O
1
2
3
4 x
2
3
4
3.
4x y > 1
4(2) 5 ?
> 1
3 >/ 1
(2, 5) is not a solution.
316
Fluid
Total
ounces of
amount
grapefruit ≥
of
juice
vitamin C
15x 12y ≥ 60
Test (0, 0).
O
2
4. Let x the fluid ounces of orange juice, and let y the
(5, 11)
5
4
1
2
3
Pre-Algebra
Chapter 8 Solutions Key
LAHPA11FLSOL_c08.indd 316
4.
4x y > 1
4(0) 0 ?
> 1
0 > 1 ✓
(0, 0) is a solution.
Copyright © Holt McDougal
All rights reserved.
2/4/09 12:51:07 PM
Chapter 8 continued
5.
4x y > 1
4(4) (4) ?
> 1
6.
4x y > 1
4(1) 3 ?
> 1
12 > 1 ✓
1 >/ 1
(4, 4) is a solution.
(1, 3) is not a solution.
7. y < 3x 1
10. y ≥ 1
Graph y 1 using a solid line.
Test (0, 0).
y≥1
0 ≥/ 1
Graph y 3x 1 using a dashed line.
Shade the half-plane that does not contain (0, 0).
Test (0, 0).
y
4
y < 3x 1
0?
< 3(0) 1
0<1 ✓
y≥1
3
2
4 3 2
O
Shade the half-plane that contains (0, 0).
2
3
4 x
2
3
4
y
4
3
2
1
y < 3x 1
1
11. (1) Let x the number of matinee tickets, and let
O
4 3 2
1
2
3
4 x
y the number of evening tickets.
Number
Cost of
Cost of of
evening
p
matinee matinee
show
tickets
3
4
8. 4x 5y ≤ 20
Graph 4x 5y 20 using a solid line.
Test (0, 0).
Number
Amount
of
≤ of gift
p
evening
certificate
tickets
5x 8y ≤ 40
(2) Graph 5x 8y 40 using a solid line.
Test (0, 0).
4x 5y ≤ 20
4(0) 5(0) ?
≤ 20
5x 8y ≤ 40
5(0) 8(0) ?
≤ 40
0 ≤ 20 ✓
Shade the half-plane that contains (0, 0).
0 ≤ 40 ✓
Shade the half-plane that contains (0, 0).
y
2
4x 5y ≤ 20
2
O
1
2
3
5
Movie Tickets
6 x
2
3
5
6
Evening tickets
1
y
6
5
4
3
2
5x 8y ≤ 40
1
0
9. x > 2
Graph x 2 using a dashed line.
Test (0, 0).
x > 2
0 1 2 3 4 5 6 7 8 9 x
Matinee tickets
(3) Sample answer: 0 matinees and 5 evening shows,
3 matinees and 3 evening shows, 6 matinees and
1 evening show
8.9 Practice and Problem Solving (pp. 463–465)
0 > 2 ✓
Shade the half-plane that contains (0, 0).
12. Sample answer: Because the inequality is >, the line
should be dashed, not solid.
y
y
4
3
3
x > 2
2
2
1
1
4 3
O
1
2
2
3
4
Copyright © Holt McDougal
All rights reserved.
LAHPA11FLSOL_c08.indd 317
3
4 x
4 3 2
O
1 2
3
4 x
3
4
5
Pre-Algebra
Chapter 8 Solutions Key
317
2/4/09 12:51:10 PM
Chapter 8 continued
13. Sample answer: The wrong half-plane is shaded. The
half-plane to the right and below the boundary should be
shaded.
y
21. y > 3x
Graph y 3x using a dashed line.
Test (1, 1).
y > 3x
1?
> 3(1)
5
4
3
2
1 > 3 ✓
Shade the half-plane that contains (1, 1).
4 3 2
O
1 2
3
4 x
y
4
3
2
3
14. No. Sample answer: The test point (0, 0) is on the line
y 2x. Whether or not a point on the boundary line is a
solution of an inequality has no bearing on which halfplane is shaded.
4 3 2
y > 3x
O
1
2
3
4 x
2
3
4
15. Sample answer: The point (5, 10) is a solution of
y ≤ x 5, but is not a solution of y < x 5.
y≤x5
10 ?
≤55
y<x5
10 ?
<55
10 ≤ 10 ✓
10 </ 10
16. y ≥ 7x 9
2
Graph y 3x 5 using a solid line.
Test (0, 0).
2
y ≥ 3x 5
4?
≥ 7(1) 9
0?
≥ 3 (0) 5
2
4≥2 ✓
0 ≥ 5 ✓
(1, 4) is a solution.
17.
2
22. y ≥ 3x 5
Shade the half-plane that contains (0, 0).
y < 10x 1
11 ?
< 10(1) 1
y
1
11 </ 11
O
(1, 11) is not a solution.
1
y≥
2
2
x
3
3
4
5
6
8 x
5
18. x ≤ 6
8 ≤/ 6
(8, 9) is not a solution.
19.
5x 8y ≥ 2
5(0) 8(3) ?
≥2
23. y ≤ 2x 3
24 ≥ 2 ✓
Graph y 2x 3 using a solid line.
(0, 3) is a solution.
Test (0, 0).
20. y < x 4
Graph y x 4 using a dashed line.
y ≤ 2x 3
0?
≤ 2(0) 3
Test (0, 0).
0 ≤/ 3
y<x4
0?
<04
Shade the half-plane that does not contain (0, 0).
y
3
2
0<4 ✓
1
Shade the half-plane that contains (0, 0).
5 4 3 2
y
6
5
y ≤ 2x 3
3
O
1 2 3 x
3
4
5
2
1
6 5
3 2
O
1
2 x
y < x 4 2
318
Pre-Algebra
Chapter 8 Solutions Key
LAHPA11FLSOL_c08.indd 318
Copyright © Holt McDougal
All rights reserved.
2/4/09 12:51:12 PM
Chapter 8 continued
24. x y ≥ 2
27. 4x 3y < 12
Graph x y 2 using a solid line.
Graph 4x 3y 12 using a dashed line.
Test (0, 0).
Test (0, 0).
x y ≥ 2
0 0?
≥ 2
4x 3y < 12
4(0) 3(0) ?
< 12
0 </ 12
0 ≥ 2 ✓
Shade the half-plane that contains (0, 0).
x y ≥ 2
y
y
3
2
2
1
1
5 4 3 2
Shade the half-plane that does not contain (0, 0).
6 5 4 3
O
1 2 x
2
4x 3y < 12
3
4
5
4
5
6
25. x 2y ≤ 6
28. y > 3
Graph x 2y 6 using a solid line.
Graph y 3 using a dashed line.
Test (0, 0).
Test (0, 0).
x 2y ≤ 6
0 2(0) ?
≤6
y > 3
0 > 3 ✓
0 ≤6 ✓
Shade the half-plane that contains (0, 0).
Shade the half-plane that contains (0, 0).
y
2
y
1
5
4
4 3 2
6 5 4 3 2
O
Test (0, 0).
Test (0, 0).
x≥1
3x 2y > 2
3(0) 2(0) ?
>2
0 ≥/ 1
4 x
Shade the half-plane that does not contain (0, 0).
0 >/ 2
y
4
3
Shade the half-plane that does not contain (0, 0).
x≥1
2
y
1
4
3
2
4 3 2
1
3
4
3
Graph x 1 using a solid line.
Graph 3x 2y 2 using a dashed line.
O
2
y > 3
29. x ≥ 1
26. 3x 2y > 2
3 2
1
4
5
6
1 x
2
3
x 2y ≤ 6
O
2
2
1
1
2
3
4
5 x
O
2
3
4 x
2
3
4
3x 2y > 2
Copyright © Holt McDougal
All rights reserved.
LAHPA11FLSOL_c08.indd 319
O
1 2 3 x
Pre-Algebra
Chapter 8 Solutions Key
319
2/4/09 12:51:14 PM
Chapter 8 continued
30. x < 4
32. ––CONTINUED––
Graph x 4 using a dashed line.
Test (0, 0).
x < 4
0 </ 4
Shade the half-plane that does not contain (0, 0).
y
x < 4
3 2
ten 1-ticket and five 2-ticket rides, fourteen 1-ticket
and three 2-ticket rides
4
33. a. y > 3x
4
Graph y 3x using a dashed line.
4
3
Test (9, 3).
2
y > 3x
4
1
7 6 5
c. Sample answer: four 1-ticket and eight 2-ticket rides,
O
3?
> 3(9)
4
1 x
3 >/ 12
2
3
4
Shade the half-plane that does not contain (9, 3).
Widescreen Format
31. y ≤ 1
Width (in.)
Graph y 1 using a solid line.
Test (0, 0).
y ≤ 1
0 ≤/ 1
Shade the half-plane that does not contain (0, 0).
y
45
40
5
0
y
4
3
4
y 3x
35
30
25
20
15
10
0 5 10 15 20 25 30 35 40 45 x
Height (in.)
2
1
4 3 2
O
1
2
3
4
2
3
b. Let x 18.
4 x
4
y > 3x
y ≤ 1
4
y > 3(18)
32. a. Let x the number of 1-ticket rides, and let y the
number of 2-ticket rides.
Number
Number
2-ticket Total
1-ticket
of
p
≤
p
of
tickets
rides
rides
tickets
tickets
1x 2y ≤ 20
x 2y ≤ 20
b. Graph x 2y 20 using a solid line.
Test (0, 0).
x 2y ≤ 20
0 2(0) ?
≤ 20
0 ≤ 20 ✓
Shade the half-plane that contains (0, 0).
2-ticket rides
Carnival Rides
y
12
10
8
6
4
2
0
x 2y ≤ 20
0 2 4 6 8 10 12 14 16 18 20 x
1-ticket rides
––CONTINUED––
320
Pre-Algebra
Chapter 8 Solutions Key
LAHPA11FLSOL_c08.indd 320
y > 24
If the height of a widescreen image is 18 inches, then
the width is greater than 24 inches.
34. a. Kite A:
1
A 2 p bh bh (12 20)9 32 p 9 288
2
288 square inches
冫hes
p
288 square
inc
1 square foot
144 square
冫hes
inc
2 square feet
Kite B:
1
A 2 p bh s 2
2
bh s 2
16 p 11 162
176 256
432
432 square inches
1 square foot
冫hes
p 432 square
inc
144 square
冫hes
inc
3 square feet
––CONTINUED––
Copyright © Holt McDougal
All rights reserved.
2/4/09 12:51:16 PM
Chapter 8 continued
34. ––CONTINUED––
37. Sample answer: It is the intersection of two half-planes,
b. Let x the number of kite A, and let y the number
of kite B.
Area of Number
Area of Number
Total
kite A p of
kite B p of
≤
area
kite A
kite B
2x 3y ≤ 48
Graph 2x 3y 48 using a solid line.
Test (0, 0).
2x 3y ≤ 48
2(0) 3(0) ?
≤ 48
0 ≤ 48 ✓
Shade the half-plane that contains (0, 0).
and consists of all points that are below and to the right
of the line y x 3 and that are also on or above and to
the right of the line y 2x 3.
8.9 Mixed Review (p. 465)
38. 8 p 8 p 8 p 8 p 8 85
5
x
40. x p x p x p x p x p x p x x7 41. 5x2 2
2b8
a
44. y 2x 3
Number of kite B
9
m n
42. 2a3b8 3
43. 9m5n4 54
yx1
y
6
5
(4, 5)
4
3
Making Kites
y
28
24
2
yx1
20
16
3 2
y 2x 3
O
2 3 4
8
4
2x 3y ≤ 48
0
0 4 8 12 16 20 24 28 x
Number of kite A
The solution is (4, 5).
45. y 3x 6
all your paper lie on the boundary line. Points that
represent solutions where you have paper left over lie
inside the shaded region, but not on the boundary line.
y<x3
4 ?
<03
4 < 3 ✓
(0, 4) is not a solution.
b. y < x 3
3?
<13
3<4 ✓
(1, 3) is a solution.
35. a.
c. y < x 3
y ≥ 2x 3
4 ?
≥ 2(0) 3
4 ≥/ 3
y ≥ 2x 3
3?
≥ 2(1) 3
3 ≥ 5 ✓
y 2x 4
y ≥ 2x 3
1?
≥ 2(2) 3
1≥1 ✓
4
2
y ≥ 2x 3
y<x3
2
y 3x 6
6 5 4 3
O
y 2x 4
1 2 x
2
(2, 0)
The solution is (2, 0).
46. x y 2
2x y 0
y x 2
y 2x
2
O
2
3
4
5
6
1 2 3 4 5 6 7 x
y 2x
(2, 4)
y x 2
The solution is (2, 4).
8.9 Standardized Test Practice (p. 465)
47. D;
y ≥ 9x 4
1 ?
≥ 9(3) 1
1 ≥/ 28
1
O
4
y
1?
< 2 3
1 </ 1
(2, 1) is not a solution.
36. y < x 3
Graph y x 3 using a dashed line.
y ≥ 2x 3
Graph y 2x 3 using a solid line.
Use the test points in Exercise 35.
y
w
2
5 x
2
12
c. Points that represent solutions where you use up
4
39. (1.2)(1.2)(1.2) (1.2)3
1 2 3 4 x
3
4
Copyright © Holt McDougal
All rights reserved.
LAHPA11FLSOL_c08.indd 321
Pre-Algebra
Chapter 8 Solutions Key
321
2/4/09 12:51:18 PM
Chapter 8 continued
48. I;
6.
y
1
6 5 4 3
O
y
5
4
1 2 x
3
2
1
O
6
7
x<8
xy<3
2 (3) ?
<3
3 ≥ 5 ✓
(1, 6) is a solution of y 8x 2.
8.
14x 2y 22
14(2) 2(3) ⱨ 22
34 22
9.
Chapter 8 Review (pp. 466–469)
3x 12y 24
3x 12y 24
3x 12(0) 24
3(0) 12y 24
3x 24
12y 24
1. Sample answer: The domain of a relation is the set of
x8
inputs, or x-coordinates. The range of a relation is the set
of outputs, or y-coordinates.
2
y }x 4
3
2
The slope is } and the y-intercept is 4.
3
3. Sample answer: The line’s slope is the ratio of the rise
and run between two points.
y 5x 2
y
5
4
0
4
2
1
322
Input
6
5
4
3
(0, 0)
O
1 2 3 4 x
2
3
(4, 3)
Pre-Algebra
Chapter 8 Solutions Key
LAHPA11FLSOL_c08.indd 322
Output
3
0
3
6
y 2x 10
y 2x 10
0 2x 10
y 2(0) 10
2x 10
y 10
x5
The x-intercept is 5, and the y-intercept is 10.
11.
f (x) 5x 2
5.
y 2
The x-intercept is 8, and the y-intercept is 2.
10.
2. Sample answer: y mx b
5 4 3 2
7
7 x
(2, 3) is not a solution of 14x 2y 22.
9≤9 ✓
(4, 3)
6
6
66 ✓
3x y ≤ 9
3(2) (3) ?
≤9
(5, 6)
5
6 ⱨ 8(1) 2
1 < 3 ✓
4.
4
7. y 8x 2
3 > 8 ✓
y ≥ 5
3
(2, 8)
8
y > 2x 4
8
2
0
3
5
3
(7, 2)
5
6
7
3 ?
> 2(2) 4
2<8 ✓
2
3
4
(2, 3) is a solution of all of the inequalities.
2
(3, 0)
1
2
Brain Game (p. 465)
Output
(2, 3)
2
3x y 6
Input
(6, 5)
20x 4y 20
20x 4y 20
20x 4(0) 20
20(0) 4y 20
20x 20
4y 20
x 1
y 5
The x-intercept is 1, and the y-intercept is 5.
rise
run
difference of y-coordinates
difference of x-coordinates
10 (7)
2 4
3
6
1
2
12. m Copyright © Holt McDougal
All rights reserved.
2/4/09 12:51:20 PM
Chapter 8 continued
rise
run
difference of y-coordinates
difference of x-coordinates
99
3 6
0
9
13. m 0
rise
run
difference of y-coordinates
difference of x-coordinates
12 4
73
16
4
14. m 23. g(x) 2x 6
g(2) 2(2) 6 10
24. y 2x 12
yx3
y
4 3 2
8 7
x
O
2
3
y 2x 12
5
6
(3, 6)
7
8
yx3
The solution is (3, 6).
25. y 2x 5
y 4x 1
y
y 2x 5
(1, 3)
3
2
4
1
15. y 3x 2
The line has a slope of 3 and a y-intercept of 2.
16. 2x 3y 6
4 3 2
O
1
4 x
2
2
y 4x 1
3y 2x 6
The solution is (1, 3).
2
y 3x 2
26. 2x y 1
2
y 3x (2)
4x 2y 22
y 2x 1
2y 4x 22
y 2x 11
2
The line has a slope of 3 and a y-intercept of 2.
y
17. 36x 9y 18
9y 36x 18
y 4x 2
The line has a slope of 4 and a y-intercept of 2.
18. Because the slope of the given line is 3, the slope of the
4x 2y 22
O
4
6
8
2 4
8 10 12 14 x
6
(3, 5)
10
2x y 1
parallel line is also 3. The y-intercept is 2.
y 3x 2
19. Because the slope of the given line is 1, the slope of the
parallel line is also 1. The y-intercept is 6.
y 1x (6)
y x 6
20. Because the slope of the given line is 9, the slope of the
parallel line is also 9. The y-intercept is 5.
y 9x 5
21. g(x) 2x 6
The solution is (3, 5).
27. y ≤ 2x 3
Graph y 2x 3 using a solid line.
Test (0, 0).
y ≤ 2x 3
0 ≤ 2(0) 3 3 ✓
Shade the half-plane that contains (0, 0).
y
g(4) 2(4) 6 2
6
5
4
When x 4, g(x) 2.
22. g(x) 2x 6
3
14 2x 6
1
8 2x
4 x
4 3
O
y ≤ 2x 3
1 2 3 4 x
2
When g(x) 14, x 4.
Copyright © Holt McDougal
All rights reserved.
LAHPA11FLSOL_c08.indd 323
Pre-Algebra
Chapter 8 Solutions Key
323
2/4/09 12:51:22 PM
Chapter 8 continued
28. y ≥ 4
2.
Graph y 4 using a solid line.
Test (0, 0).
y≥4
0≥4 ✓
Shade the half-plane that contains (0, 0).
2
3
Output
3
1
6
5
8
7
9
9
(8, 1)
1 2 3 4 5 6 7 8 9 x
The relation is a function because every input is paired
with exactly one output.
y ≥ 4
3. y 7 2x
1 ⱨ 7 2(5)
6
7
1 3
(5, 1) is not a solution.
29. 3x y > 6
y 7 2x
Graph 3x y 6 using a dashed line.
5 ⱨ 7 2(6)
Use (0, 0) as a test point.
5 5 ✓
3x y > 6
3(0) 0 ?
> 6
(6, 5) is a solution.
y 7 2x
0 > 6 ✓
3 ⱨ 7 2(2)
Shade the half-plane that contains (0, 0).
33 ✓
y
(2, 3) is a solution.
1
O
1
2
3
4 x
4.
y 3x 4
1 ⱨ 3(1) 4
2
3x y > 6
1 1 ✓
(1, 1) is a solution.
6
7
y 3x 4
4 ⱨ 3(0) 4
4 4 ✓
Chapter 8 Test (p. 470)
y
4
Input
Output
0
2
1
0
1
2
3
(0, 2)
2
4 3 2
Input
4 x
5
1.
(3, 5)
O
1
2
3
4 3
(6, 7)
1
1
O
(9, 9)
2
y
4 3 2
y
9
8
7
6
5
4
3
1
(0, 1)
(0, 0)
O
1
2
3
4 x
(0, 1)
2
(0, 2)
3
4
The relation is not a function because the input 0 is paired
with 5 outputs, 2, 1, 0, 1, and 2.
(0, 4) is a solution.
y 3x 4
34 ⱨ 3(10) 4
34 34
(10, 34) is not a solution.
5. x y 4
xy4
x04
0y4
x4
y4
The x-intercept is 4, and the y-intercept is 4.
y
6
5
4
3
(0, 4)
2
1
2
O
(4, 0)
1
2
3
4
5
6 x
2
324
Pre-Algebra
Chapter 8 Solutions Key
LAHPA11FLSOL_c08.indd 324
Copyright © Holt McDougal
All rights reserved.
2/4/09 12:51:24 PM
Chapter 8 continued
6.
4x 3y 24
4x 3y 24
4x 3(0) 24
4(0) 3y 24
4x 24
3y 24
x6
y 8
The x-intercept is 6, and the y-intercept is 8.
y
O
x
1
2
3
4
(6, 0)
5
2
3
4
5
6
7
(0, 8)
5
y 2x 10
5
5
y 2(0) 10
y 2x 10
7.
5
0 2x 10
y 10
5
2x 10
x4
The x-intercept is 4, and the y-intercept is 10.
y
2
6 4
(4, 0)
O
2
6
8 10 x
4
6
8
(0, 10)
rise
run
difference of y-coordinates
difference of x-coordinates
32
04
1
4
1
4
rise
11. m run
difference of y-coordinates
difference of x-coordinates
50
2 (2)
5
0
10. m The slope is undefined.
rise
run
difference of y-coordinates
difference of x-coordinates
77
10 4
0
6
11. m 0
4
8.
y 3x 6
y 3x 6
0 3x 6
y 3(0) 6
3x 6
y6
x 2
The x-intercept is 2, and the y-intercept is 6.
y
7
6
13. y 3x 7
4
The line has a slope of 3 and a y-intercept of 7.
y
2
O
1
2
3
4
6 x
2
3
4
5
(3, 3)
4
(0, 7)
(0, 6)
3
4
3
2
(2, 0)
5 4 3
14. y 5x 1
1
O
1
2
3 x
The line has a slope of 5 and a y-intercept of 1.
y
6
rise
run
difference of y-coordinates
difference of x-coordinates
7 (3)
10 8
10
2
(1, 6)
5
9. m 4
3
5
2
(0, 1) 1
4 3 2
O1
2
3
4 x
5
Copyright © Holt McDougal
All rights reserved.
LAHPA11FLSOL_c08.indd 325
Pre-Algebra
Chapter 8 Solutions Key
325
2/4/09 12:51:26 PM
Chapter 8 continued
15. 6x y 2
18. (0, 3), (4, 9)
y 6x 2
The line has a slope of 6 and a y-intercept of 2.
b3
y
5
4
3
y mx b
(1, 4)
3
f (x) x 3
2
2
6
1
3 2
2
O
3
4
19. (0, 6), (15, 9)
5 x
9 (6) 3
1
m 15 0
15
5
(0, 2) 1
b 6
16. 6x 5y 10
y mx b
5y 6x 10
6
y 5x 2
6
The line has a slope of 5 and a y-intercept of 2.
(5, 4)
4
3
10 (5) 15
m 0 (4)
4
2
b 10
6
1
2
O
3
4
y mx b
15
h(x) x 10
4
21. x 5y 10
6 x
(0, 2)
5
17. a.
y
410
400
390
y
1
5x
1
2
y 5x 1
y
2
4 3 2
0
1
2
3 4 5
Months
6
7
O
x 5y 5
1 2
rise
m run
difference of y-coordinates
difference of x-coordinates
401 352
50
4 x
x 5y 10
4
The system has no solution.
22. 3x y 7
9.8
8
7
y 3x 7
Pre-Algebra
Chapter 8 Solutions Key
4
3
2
1
y 9.8x 352
About 421 televisions were sold during the 7th month.
y 3x 7
y 3x 7
The y-intercept is 352
c. y 9.8x 352 9.8(7) 352 420.6
3x y 7
y 3x 7
49
5
LAHPA11FLSOL_c08.indd 326
3
x
b. Sample answer: Using (0, 352) and (5, 401):
326
5y x 5
4
3
380
370
360
350
0
x 5y 5
5y x 10
Television Sales
Televisions
1
g(x) x (6)
5
1
g(x) x 6
5
20. (4, 5), (0, 10)
y
5
2
93 6 3
m 40 4 2
6 5 4 3
O
1 2 x
The system has infinitely many solutions.
Copyright © Holt McDougal
All rights reserved.
2/4/09 12:51:28 PM
Chapter 8 continued
23. 2x y 5
x 2y 10
y 2x 5
2y x 10
1
y 2x 5
y 2x 5
y
1
3 2
O
1
3
4
5 x
26. x 2y > 6
Graph x 2y 6 using a dashed line.
Test (0, 0).
x 2y > 6
0 2(0) ?
>6
0 >/ 6
2x y 5
2
3
4
Shade the half-plane that does not contain (0, 0).
y
x 2y 10
(0, 5)
5
4
x 2y > 6
2
1
The solution is (0, 5).
O
24. x < 7
x
1
2
3
4
5
6
2
3
Graph x 7 using a dashed line.
Test (0, 0).
x<7
Chapter 8 Standardized Test (p. 471)
0<7 ✓
Shade the half-plane that contains (0, 0).
y
1. B
2. H; The vertical line x 4 is not a function because it
does not pass the vertical line test.
4
3
3. A; x 4y 24
x<7
2
0 4y 24
1
O
1
2
3
4
5
6
4y 24
8 x
y 6
4. G; x 4y 24
4y x 24
25. y ≤ 3x 5
1
Graph y 3x 5 using a solid line.
Test (0, 0).
y 4x 6
5. B; f(x) 2x 1
f(5) 2(5) 1 9
y ≤ 3x 5
0 ≤/ 3(0) 5 5
6. I;
Shade the half-plane that does not contain (0, 0).
y
2
1
3 2
O
2
3
4
5
3x y 11
3(4) 1 ⱨ 11
11 11 ✓
(4, 1) is a solution.
y 2x 9
1 ⱨ 2(4) 9
11 ✓
7. C
1 2 3 4 5 x
y ≤ 3x 5
8. 4y x 24
4y 0 24
4y 24
y 6
So the y-intercept is 6.
rise
run
9. m difference of y-coordinates
difference of x-coordinates
6 2
}
42
8
}
2
4
Copyright © Holt McDougal
All rights reserved.
LAHPA11FLSOL_c08.indd 327
Pre-Algebra
Chapter 8 Solutions Key
327
2/4/09 12:51:30 PM
Chapter 8 continued
10. The slope of the given line is 4, so the slope of a
perpendicular line is
Problem Solving Practice (p. 473)
1
.
4
4p4 44
1. Sample answer: , , and 44 44
4p4 44
11. y 3x
2. Let t the number of years using the refrigerators.
y 3(24)
The cost a for Refrigerator A is: a 600 35t
y 72
The cost b for Refrigerator B is: b 800 40t
So the pool is 72 feet in length.
12. A; 4x 2y 6
Find the year when the total costs a and b are the same.
y 2x 6
ab
2y 4x 6
y 2x 3
600 35t 800 40t
600 800 5t
y
8
200 5t
y 2x 6
40 t
5
The answer is 40 years which does not make
sense. There is no solution. The total costs of the two
refrigerators will never be the same.
4x 2y 6
2
1
4 3 2
O
3. (1) Write an equation.
1
3
4 x
Let n the number of coins in the jar. When you
and your sister split the coins, let x the number of
coins each of you receives. There is one remaining, so
n 2x 1.
The system has no solution.
1
13. 2; 2.
Sample answer: y ax 6
x 2y 4
2y x 4
1
y 2x 2
1
The slope of the given line is 2, so the slope of a
parallel line is also
1
2.
So, a 1
2.
of video games.
Amount
Rental fee Number
Rental Number
fee for p of
for video p of video of gift
card
games
movies movies
games
4x 5y 100
4x 5y 100
4x 5y 100
4x 5(0) 100
4(0) 5y 100
4x 100
5y 100
x 25
y 20
The x-intercept is 25, and the y-intercept is 20.
Video games
Movie and Video Rental
y
25
(0, 20)
20
15
10
5
(25, 0)
0
0 5 10 15 20 25 30 35 x
Movies
c. Sample answer: Choose 3 points on the line: (0, 20),
(10, 12), and (25, 0).
You can rent 0 movies and 20 video games, 10 movies
and 12 video games, or 25 movies and 0 video games.
Pre-Algebra
Chapter 8 Solutions Key
LAHPA11FLSOL_c08.indd 328
3y 2x 1
2
The slope of a perpendicular line is 2. So, a 2.
328
Write an equation giving y as a function of x.
1
y 3x 3
14. a. Let x the number of movies, and let y the number
b.
When your cousin is included, let y the number of
coins each of you receives. None are remaining, so
n 3y.
(2) Make a graph.
2
1
Graph y 3x 3. Label points with whole-number
coordinates.
Coins for you, your
sister, and your cousin
6
y
7
6
5
4
3
2
1
0
(10, 7)
(7, 5)
(4, 3)
(1, 1)
0 1 2 3 4 5 6 7 8 9 10 x
Coins for you and your sister
(3) Solve the problem
Sample answer: Use the equation n 3y and the
y-coordinates of the labeled points to find some
possible number of coins in the jar.
y
Substitution
n
1
n 3(1)
3
3
n 3(3)
9
5
n 3(5)
15
7
n 3(7)
21
Some possible numbers of coins in the jar are 3, 9,
15, and 21.
Copyright © Holt McDougal
All rights reserved.
2/4/09 12:51:32 PM
Chapter 8 continued
4. Sample answer: 16 17 12
11 15 19
18 13 14
Number of loaves of pumpkin bread
3
1
Graph y 2x 2. Label the points with
y
(0, 12)
12
y
8
Bun packages used
Let x the number of pumpkin pies you make and let
y the number of loaves of pumpkin bread you make.
You can write an equation giving y as a function of x.
1.5x 1y 12
y 1.5x 12
(2) Make a graph.
Graph y 1.5x 12. Label the points with
whole-number coordinates.
(5, 8)
7
6
5
(3, 5)
4
3
2
1
0
(1, 2)
0 1 2 3 4 5 6 7 8 x
Hamburger packages used
(3) Solve the problem
11
Use the equation h 12x 7 and the x-coordinates
of the labeled points to find some possible numbers
of hamburgers eaten.
(2, 9)
9
(2) Make a graph.
whole-number coordinates.
5. (1) Write an equation.
10
6. ––CONTINUED––
8
7
(4, 6)
6
Sample answer:
x
Substitution
n
1
h 12(1) 7
19
3
h 12(3) 7
43
5
h 12(5) 7
67
5
4
(6, 3)
3
2
1
0
(8, 0)
0 1 2 3 4 5 6 7 8 x
Number of pumpkin pies
(3) Solve the problem
Sample answer: Using the points on the graph, you
could make no pumpkin pies and 12 loaves of bread,
2 pies and 9 loaves of bread, or 4 pies and 6 loaves
of bread.
6. (1) Write an equation.
Let x be the number of complete packages of
hamburgers used. The total number h of hamburgers
eaten is the sum of the 12x hamburgers in the
complete packages used and the 12 5 7
hamburgers used in the last package.
h 12x 7
Let y be the number of complete packages of buns
used. The total number b of buns eaten is the sum
8y buns in the complete packages used and the
8 5 3 buns used in the last package.
b 8y 3
Assume that the same number of hamburgers and
buns were eaten. Then you can write an equation
giving y as a function of x.
bh
8y 3 12x 7
8y 12x 4
12
Some possible numbers of hamburgers eaten are 19,
43, and 67.
7. (1) Write an equation.
Let y the length of the pool and let x the width
of the pool. The pool is rectangular.
A xy
15,000 xy
15,000
y
x
(2) Make a graph.
15,000
Use a graphing calculator to graph y .
x
Use the trace feature to find a few points with
whole-number coordinates.
(3) Solve the problem
Sample answer: The pool could be 40 feet by 375
feet, 50 feet by 300 feet, or 100 feet by 150 feet.
4
y 8 x 8
3
1
y 2x 2
––CONTINUED––
Copyright © Holt McDougal
All rights reserved.
LAHPA11FLSOL_c08.indd 329
Pre-Algebra
Chapter 8 Solutions Key
329
2/4/09 12:51:34 PM
Chapter 8 continued
8. No. Sample answer: Each domino must cover a red
square and a black square. There are 32 red squares and
30 black squares, so there will be two red squares left
over for any placement of 30 dominoes. No two red
squares are adjacent, so there is no solution.
9. a. Because 9 10 19 and 10 11 21, there is no
pair of consecutive integers whose sum is 20.
b. The two consecutive integers could be both positive or
both negative because the product is positive.
4 p 5 20
4(5) 20
So, the two consecutive integers are 4 and 5 or 4
and 5.
330
Pre-Algebra
Chapter 8 Solutions Key
LAHPA11FLSOL_c08.indd 330
Copyright © Holt McDougal
All rights reserved.
2/4/09 12:51:36 PM