Algebra I – Study Guide
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____
1. Which graph represents a function?
y
a.
–5
–4 –3
4
4
3
3
2
2
1
1
–2 –1
–1
1
2
3
4
–4 –3
–5
5 x
–4 –3
–2 –1
–1
–2
–2
–3
–3
–4
–4
–5
–5
d.
y
–5
y
5
b.
____
c.
5
5
4
4
3
3
2
2
1
1
1
2
3
4
5 x
2
3
4
5 x
1
2
3
4
5 x
y
5
–2 –1
–1
1
–5
–4 –3
–2 –1
–1
–2
–2
–3
–3
–4
–4
–5
–5
2. Temperature changes throughout the hours of a day. Early in the morning, temperature increases slowly. At
noon, the temperature rises sharply. During the afternoon, the temperature stays the same for several hours.
As night falls, the temperature decreases slightly. Choose the graph that best represents this situation.
1
c.
Temperature
Temperature
a.
Hours
Hours
d.
Temperature
Temperature
b.
Hours
Hours
Matching
Match each vocabulary term with its definition.
a. linear function
b. x-axis
c. x-intercept
d. y-intercept
e. y-axis
f. rate of change
g. linear equation
h. slope
____
____
____
____
____
____
3. a ratio that compares the amount of change in the dependent variable to the amount of change in the
independent variable
4. the x-coordinate of the point where a graph intersects the x-axis
5. a function whose graph forms a straight line
6. an equation that can be written in the form of
, where A, B, and C are real numbers, and A and B
are not both zero
7. a measure of the steepness of a line
8. the y-coordinate of the point where a graph intersects the y-axis
2
Short Answer
9. Solve
.
10. Solve
.
11. A toy company's total payment for salaries for the first two months of 2005 is $21,894. Write and solve an
equation to find the salaries for the second month if the first month’s salaries are $10,205.
12. The range of a set of scores is 23, and the lowest score is 33. Write and solve an equation to find the highest
score. (Hint: In a data set, the range is the difference between the highest and the lowest values.)
13. Solve
.
14. Solve 3n = 42.
15. Solve
16. If
.
, find the value of
17. Solve
.
.
18. Solve
.
19. If 8y – 8 = 24, find the value of 2y.
20. Solve
.
21. Solve
. Tell whether the equation has infinitely many solutions or no solutions.
22. A professional cyclist is training for the Tour de France. What was his average speed in miles per hour if he
rode the 120 miles from Laval to Blois in 4.7 hours? Use the formula
, and round your answer to the
nearest tenth.
23. The formula for the resistance of a conductor with voltage V and current I is
24. Solve
. Solve for V.
for x.
25. The price of a train ticket from Atlanta to Oklahoma City is normally $117.00. However, children under the
age of 16 receive a 70% discount. Find the sale price for someone under the age of 16.
26. Solve
.
27. Graph the inequality m  –3.4.
28. Write the inequality shown by the graph.
–7 –6 –5 –4 –3 –2 –1
0
1
2
3
4
5
6
7
m
29. Solve the inequality n + 6  –1.5 and graph the solutions.
30. Solve the inequality
 3 and graph the solutions.
31. Solve the inequality 2m  18 and graph the solutions.
3
 2 and graph the solutions.
32. Solve the inequality
33. Marco’s Drama class is performing a play. He wants to buy as many tickets as he can afford. If tickets cost
$2.50 each and he has $14.75 to spend, how many tickets can he buy?
34. Solve the inequality n – 4  3 and graph the solutions.
35. Solve and graph
.
36. Mrs. Williams is deciding between two field trips for her class. The Science Center charges $135 plus $3 per
student. The Dino Discovery Museum simply charges $6 per student. For how many students will the Science
Center charge less than the Dino Discovery Museum?
37. Solve the inequality and graph the solution.
38. Solve and graph the solutions of the compound inequality
.
39. Solve and graph the compound inequality.
OR
40. Write the compound inequality shown by the graph.
–10 –9 –8
–7 –6
–5 –4
–3 –2
–1
0
1
41. Which of the following is a solution of
2
3
4
5
6
AND
7
8
9
?
Water level
42. Write a possible situation for the graph.
Time
43. Find the x- and y-intercepts.
4
10 x
y
10
8
6
4
2
–10 –8
–6
–4
–2
–2
2
4
6
8
10
x
–4
–6
–8
–10
44. Find the x- and y-intercepts of
.
45. A clothing manufacturer needs 2.4 yards of fabric to make a jacket and 1.6 yards of fabric to make a matching
skirt. The number of jackets, x, and coats, y, that can be made from a 48-yard bolt of fabric can be represented
by the equation 2.4x + 1.6y = 48. Graph the function and find its intercepts. What does each intercept
represent?
46. Use intercepts to graph the line described by the equation
47. Find the slope of the line that contains
and
.
.
48. Tara creates a budget for her weekly expenses. The graph shows how much money is in the account at
different times. Find the slope of the line. Then tell what rate the slope represents.
2750
2500
(4, 2400)
Amount ($)
2250
(12, 2000)
2000
1750
1500
1250
1000
750
500
250
2
4
6
8 10 12 14 16 18 20 22
Time (weeks)
49. Find the slope of the line described by x – 3y = –6.
50. Write the equation that describes the line with slope = 2 and y-intercept =
3
2
in slope-intercept form.
51. Write the equation that describes the line in slope-intercept form.
slope = 4, point (3, –2) is on the line
52. Write the equation
in slope-intercept form. Then graph the line described by the equation.
5
53. The water level of a river is 34 feet and it is receding at a rate of 0.5 foot per day. Write an equation that
represents the water level, w, after d days. Identify the slope and y-intercept and describe their meanings. In
how many days will the water level be 26 feet?
54. Graph the line with a slope of
2
3
that contains the point (3, –7).
55. Write an equation in point-slope form for the line that has a slope of 6 and contains the point (–8, –7).
56. Write an equation in slope-intercept form of the line with slope  that contains the point (2, 3).
57. Write an equation in slope-intercept form for the line that passes through (3, 7) and (7, 4).
58. The cost to fill a car’s tank with gas and get a car wash is a linear function of the capacity of the tank. The
costs of a fill-up and a car wash for three different customers are shown in the table. Write an equation for the
function in slope-intercept form. Then, find the cost of a fill-up and a car wash for a customer with a truck
whose tank size is 22 gallons.
Tank size (gal)
(x)
11
15
17
Total cost ($)
f(x)
21.45
28.25
31.65
59. A linear function has the same y-intercept as
intercept and slope of the linear function.
and its graph contains the point
6
. Find the y-
Algebra I
Answer Section
MULTIPLE CHOICE
1. ANS: D
For a graph to represent a function it must
pass the vertical line test.
y
5
4
Since no vertical line will intersect this graph
at more than one point, this graph represents
a function.
3
2
1
–5
–4
–3
–2
–1
–1
1
2
3
4
5
x
–2
–3
–4
–5
Feedback
A
B
C
D
A vertical line can cross this graph more than once.
For a graph to represent a function it must pass the vertical line test.
A vertical line can cross this graph more than once.
Correct!
PTS: 1
DIF: Advanced
TOP: 4-2 Relations and Functions
2. ANS: D
Only graph D contains the required features in the correct order.
Key phrases
Segment should be...
Shown in
increases slowly
slanting upward
all graphs
rises sharply
slanting upward more steeply
graphs B, C, and D
graphs B and D (also in graphs A and
stays the same
horizontal
C, but out of order)
decreases slightly
slanting downward
graphs A and D
Feedback
A
B
C
D
"Rises sharply" indicates that the temperature moves up steeply following a slower
increase in the morning.
"Decreases slightly" indicates a fall in temperature.
The temperature "stays the same" before the final change in temperature at night.
Correct!
PTS: 1
NAT: 12.5.2.b
DIF: Basic
REF: Page 230
TOP: 4-1 Graphing Relationships
7
OBJ: 4-1.1 Relating Graphs to Situations
MATCHING
3. ANS:
TOP:
4. ANS:
TOP:
5. ANS:
TOP:
6. ANS:
TOP:
7. ANS:
TOP:
8. ANS:
TOP:
F
PTS: 1
5-3 Rate of Change and Slope
C
PTS: 1
5-2 Using Intercepts
A
PTS: 1
5-1 Identifying Linear Functions
G
PTS: 1
5-1 Identifying Linear Functions
H
PTS: 1
5-3 Rate of Change and Slope
D
PTS: 1
5-2 Using Intercepts
DIF: Basic
REF: Page 310
DIF: Basic
REF: Page 303
DIF: Basic
REF: Page 296
DIF: Basic
REF: Page 296
DIF: Basic
REF: Page 311
DIF: Basic
REF: Page 303
SHORT ANSWER
9. ANS:
p = 22
Since 6 is subtracted from p, add 6 to both sides to undo the
subtraction.
Check:
To check your solution, substitute 22 for p in the original
equation.
PTS: 1
DIF: Basic
REF: Page 77
OBJ: 2-1.1 Solving Equations by Using Addition
TOP: 2-1 Solving Equations by Adding or Subtracting
10. ANS:
s = 42
NAT: 12.5.4.a
KEY: equation | solving | subtraction
Since 6 is added to s, subtract 6 from both sides to undo the addition.
Check:
To check your solution, substitute 42 for s in the original equation.
PTS: 1
DIF: Basic
REF: Page 78
8
OBJ: 2-1.2 Solving Equations by Using Subtraction
TOP: 2-1 Solving Equations by Adding or Subtracting
11. ANS:
The salaries for the second month are $11,689.
First month
Second month
Added
salaries
to
salaries
b
b + x = 21,894
10,205 + x = 21,894
–10,205
–10,205
+
x
NAT: 12.5.4.a
KEY: equation | solving | addition
is
21,894
=
21,894
Write an equation to represent the relationship.
Substitute 10,205 for b. Since 10,205 is added to x, subtract
10,205 from both sides to undo the addition.
The salaries for the second month are $11,689.
PTS: 1
NAT: 12.5.3.b
12. ANS:
DIF: Average
REF: Page 79
OBJ: 2-1.4 Application
TOP: 2-1 Solving Equations by Adding or Subtracting
The highest score is 56.
highest score
minus
h
–
lowest score
l
equals
=
score range
23
Write an equation to represent the relationship.
Substitute 33 for l.
Solve the equation.
PTS: 1
DIF: Advanced
NAT: 12.5.3.b
TOP: 2-1 Solving Equations by Adding or Subtracting
13. ANS:
q = 205
Since q is divided by 5, multiply both sides by 5 to undo the
division.
q = 205
Check:
To check your solution, substitute 205 for q in the original
equation.
PTS: 1
DIF: Basic
REF: Page 84
9
OBJ: 2-2.1 Solving Equations by Using Multiplication
NAT: 12.5.4.a
TOP: 2-2 Solving Equations by Multiplying or Dividing
KEY: equation | multiplication | solving
14. ANS:
n = 14
3n = 42
Since n is multiplied by 3, divide both sides by 3 to undo the
multiplication.
Check:
3n = 42
To check your solution, substitute 14 for n in the original equation.
PTS: 1
DIF: Basic
REF: Page 85
OBJ: 2-2.2 Solving Equations by Using Division
TOP: 2-2 Solving Equations by Multiplying or Dividing
15. ANS:
The reciprocal of
NAT: 12.5.4.a
KEY: equation | solving | multiplication
is
multiply both sides by
. Since is multiplied by
.
PTS: 1
DIF: Basic
REF: Page 85
OBJ: 2-2.3 Solving Equations That Contain Fractions
TOP: 2-2 Solving Equations by Multiplying or Dividing
16. ANS:
–5
NAT: 12.5.4.a
Solve the equation.
Substitute 8 for x and simplify.
PTS: 1
DIF: Advanced
NAT: 12.5.4.a
TOP: 2-2 Solving Equations by Multiplying or Dividing
17. ANS:
a = –15
First x is multiplied by –2. Then 14 is added.
Work backward: Subtract 14 from both sides.
Since x is multiplied by –2, divide both sides by –2 to undo the
multiplication.
10
,
PTS: 1
NAT: 12.5.4.a
18. ANS:
DIF: Basic
REF: Page 92
OBJ: 2-3.1 Solving Two-Step Equations
TOP: 2-3 Solving Two-Step and Multi-Step Equations
Use the Commutative Property of Addition.
Combine like terms.
Since 10 is added to 17a, subtract 10 from both sides to undo
the addition.
Since a is multiplied by 17, divide both sides by 17 to undo the
multiplication.
PTS: 1
DIF: Average
REF: Page 93
OBJ: 2-3.3 Simplifying Before Solving Equations
NAT: 12.5.3.c
TOP: 2-3 Solving Two-Step and Multi-Step Equations
19. ANS:
8
8y – 8 = 24
Add 8 to both sides of the equation.
+8 +8
8y = 32
8y =
8
y=
2(4) =
32
8
4
8
Divide both sides by 8.
Apply 4 to 2y.
PTS: 1
DIF: Average
REF: Page 95
OBJ: 2-3.5 Solving Equations to Find an Indicated Value
TOP: 2-3 Solving Two-Step and Multi-Step Equations
20. ANS:
To collect the variable terms on one side, subtract 50q from both
sides.
Since 81 is subtracted from 2q, add 81 to both sides to undo the
subtraction.
Since q is multiplied by 2, divide both sides by 2 to undo the
multiplication.
11
PTS: 1
DIF: Average
REF: Page 100
OBJ: 2-4.1 Solving Equations with Variables on Both Sides
NAT: 12.5.4.a
TOP: 2-4 Solving Equations with Variables on Both Sides
21. ANS:
Infinitely many solutions
Combine like terms on each side of the equation before collecting variable terms on one side.
If you get an equation that is always true, the original equation is an identity, and it has infinitely many
solutions.
If you get a false equation, the original equation is a contradiction, and it has no solutions.
PTS: 1
DIF: Average
REF: Page 102
OBJ: 2-4.3 Infinitely Many Solutions or No Solutions
TOP: 2-4 Solving Equations with Variables on Both Sides
22. ANS:
25.5 mph
NAT: 12.5.4.a
Divide both sides by t.
Substitute the known values.
Simplify. Round to the nearest tenth.
PTS: 1
NAT: 12.5.4.f
23. ANS:
V = Ir
DIF: Average
REF: Page 107
TOP: 2-5 Solving for a Variable
OBJ: 2-5.1 Application
Locate V in the equation.
Since V is divided by I, multiply both sides by I to undo the division.
PTS: 1
DIF: Basic
REF: Page 108
OBJ: 2-5.2 Solving Formulas for a Variable
NAT: 12.5.4.f
TOP: 2-5 Solving for a Variable
KEY: literal equation | solving | variables
24. ANS:
Add z to both sides.
Divide both sides by 4.
12
PTS: 1
DIF: Basic
REF: Page 108
OBJ: 2-5.3 Solving Literal Equations for a Variable
NAT: 12.5.4.f
TOP: 2-5 Solving for a Variable
25. ANS:
$35.10
Method 1 A discount is percent decrease. So find $117.00 decreased by 70%.
Find 70% of $117.00. This is the amount of the discount.
Subtract 81.90 from 117.00. This is the sale price for children
under the age of 16.
Method 2 Subtract percent discount from 100%.
Children under the age of 16 pay 30% of the regular price,
$117.00.
Find 30% of 117.00. This is the sale price for children under
the age of 16.
PTS: 1
DIF: Average
REF: Page 139
OBJ: 2-10.3 Discounts
NAT: 12.1.4.d
TOP: 2-10 Percent Increase and Decrease
KEY: percent change | percent decrease | percent increase
26. ANS:
x = 13 or x = –1
Divide both sides by 7.
What numbers are 7 units from 0?
Case 1:
x–6=7
Case 2:
x – 6 = –7
Rewrite the equation as two cases.
The solutions are x = 13 or x = –1.
PTS: 1
DIF: Average
REF: Page 294
OBJ: 2-Ext.1 Solving Absolute-Value Equations
TOP: 2-Ext Solving Absolute-Value Equations
27. ANS:
–5 –4 –3 –2 –1
0
1
2
3
4
5
The graph should start at the given value. A > or < graph has an empty circle at that value. A or graph has
a solid circle at that value. A > or graph has an arrow to the right, and a < or graph has an arrow to the
left.
PTS: 1
DIF: Basic
REF: Page 168
OBJ: 3-1.2 Graphing Inequalities
NAT: 12.5.4.c
TOP: 3-1 Graphing and Writing Inequalities
KEY: graph | inequality | number line
MSC: graph | inequality | number line
28. ANS:
m  –3
Use the variable m. The arrow points to the right, so use either > or . The solid circle at –3 means that –3 is a
solution, so use .
13
PTS: 1
DIF: Basic
REF: Page 170
OBJ: 3-1.3 Writing an Inequality from a Graph
TOP: 3-1 Graphing and Writing Inequalities
29. ANS:
n  –7.5
–10 –8 –6 –4 –2
0
2
4
6
n + 6  –1.5
–6 –6
n  –7.5
8
NAT: 12.5.4.c
10
Subtract 6 on both sides to isolate n.
–10 –8 –6 –4 –2
0
2
4
6
8
10
Use a solid circle when the value is included in the graph, such as with or  Use an empty circle when the
value is not included, such as with > or <.
PTS: 1
DIF: Basic
REF: Page 174
OBJ: 3-2.1 Using Addition and Subtraction to Solve Inequalities
NAT: 12.5.4.a
TOP: 3-2 Solving Inequalities by Adding and Subtracting
KEY: addition | inequality | subtraction | solving
MSC: addition | inequality | subtraction | solving
30. ANS:
x24
0
5
10
15
20
25
30
35
40
45
50
3
Multiply both sides by 8 to isolate x.
 3(8)
x  24

0
5
10
15
20
25
30
35
40
45
50
Use a solid circle when the value is included in the graph, such as with or  Use an empty circle when the
value is not included, such as with > or <.
PTS:
OBJ:
TOP:
MSC:
31. ANS:
m  9
–1
1
DIF: Basic
REF: Page 180
3-3.1 Multiplying or Dividing by a Positive Number
3-3 Solving Inequalities by Multiplying and Dividing
solving | inequality | graph
0
1
2
3
4
5
6
7
8
9
10
11
2m  18

Divide both sides by 2 to isolate m.
14
NAT: 12.5.4.c
KEY: solving | inequality | graph
m9
Use a solid circle when the value is included in the graph, such as with or  Use an empty circle when the
value is not included, such as with > or <.
–1
PTS:
OBJ:
TOP:
MSC:
32. ANS:
z  –8
0
1
2
3
4
5
6
7
8
9
10
11
1
DIF: Basic
REF: Page 180
3-3.1 Multiplying or Dividing by a Positive Number
3-3 Solving Inequalities by Multiplying and Dividing
solving | inequality | graph
–10 –8 –6 –4 –2
0
2
4
6
8
NAT: 12.5.4.c
KEY: solving | inequality | graph
10
2
Multiply both sides by –4 to isolate z. When you multiply by a
negative number, reverse the inequality symbol.
 2(–4)
z  –8
Use a solid circle when the value is included in the graph, such as with or  Use an empty circle when the
value is not included, such as with > or <.
–10 –8 –6 –4 –2
0
2
4
6
8
10
PTS: 1
DIF: Average
REF: Page 182
OBJ: 3-3.2 Multiplying or Dividing by a Negative Number
TOP: 3-3 Solving Inequalities by Multiplying and Dividing
KEY: inequality | solving | multiplication | division
MSC: inequality | solving | multiplication | division
33. ANS:
5 tickets
NAT: 12.5.3.c
Divide both sides by the ticket price. The inequality symbol does not
change.
Simplify.
5 is the largest whole number less than 5.9.
PTS: 1
NAT: 12.5.4.c
34. ANS:
n  –7
–10 –8 –6 –4 –2
DIF: Average
REF: Page 182
OBJ: 3-3.3 Application
TOP: 3-3 Solving Inequalities by Multiplying and Dividing
0
2
4
6
8
10
Use inverse operations to undo the operations in the inequality one at a time.
n – 4  3
n  –7
15
–10 –8 –6 –4 –2
0
2
4
6
8
10

Use a solid circle when the value is included in the graph, such as with or  Use an empty circle when the
value is not included, such as with > or <.
PTS:
OBJ:
TOP:
MSC:
35. ANS:
x<5
1
DIF: Basic
REF: Page 188
3-4.1 Solving Multi-Step Inequalities
3-4 Solving Two-Step and Multi-Step Inequalities
solving | two-step inequality
–12 –11 –10 –9 –8 –7 –6 –5 –4 –3 –2 –1
0
1
2
3
4
5
NAT: 12.5.4.a
KEY: solving | two-step inequality
6
7
8
9
10 11 12
Subtract 3x from both sides to collect the x terms on one side of the
inequality symbol.
Divide both sides by 3.
3x < 15
x<5
–12 –11 –10 –9 –8 –7 –6 –5 –4 –3 –2 –1
0
1
2
3
4
5
PTS: 1
DIF: Basic
REF: Page 194
OBJ: 3-5.1 Solving Inequalities with Variables on Both Sides
TOP: 3-5 Solving Inequalities with Variables on Both Sides
MSC: multistep inequality | solving | word problem
36. ANS:
More than 45 students
Science
plus
$3
per
student
is less
Center fee
than
$135
+
$3
s
<
6
7
8
9
10 11 12
NAT: 12.5.4.c
$12
$6
per
student
s
135 + 3s < 6s
– 3s – 3s
135
< 3s
<
45 < s
If 45 < s, then s > 45. The Science Center charges less if there are more than 45 students.
PTS: 1
DIF: Average
REF: Page 195
OBJ: 3-5.2 Application
NAT: 12.5.4.a
TOP: 3-5 Solving Inequalities with Variables on Both Sides
KEY: multistep inequality | solving | word problem
37. ANS:
16
–9 –8 –7 –6 –5 –4 –3 –2 –1
0
1
2
3
4
5
6
7
8
9
On the left side, combine the two terms. On the right side, distribute 1.5.


Subtract the 1.5x from both sides of the inequality.
6

Divide both sides of the inequality by
3
. Reverse the inequality symbol.
PTS: 1
DIF: Average
REF: Page 195
OBJ: 3-5.3 Simplifying Each Side Before Solving
TOP: 3-5 Solving Inequalities with Variables on Both Sides
38. ANS:
AND
0
1
2
3
4
NAT: 12.5.4.c
5
AND
Write the compound inequality using AND.
Solve each simple inequality.
Divide to undo the multiplication.
AND
First, graph the solutions of each simple inequality. Then, graph the intersection by finding where the two
graphs overlap.
PTS: 1
DIF: Average
REF: Page 203
OBJ: 3-6.2 Solving Compound Inequalities Involving AND
TOP: 3-6 Solving Compound Inequalities
39. ANS:
OR
–10 –9
–8 –7 –6 –5 –4
–3 –2 –1
0
1
2
3
4
First solve each simple inequality to obtain
union of the graph of
and the graph of
–10 –9
–8 –7 –6 –5 –4
–3 –2 –1
0
1
2
3
5
6
7
NAT: 12.5.4.c
8
9
10
s
OR
. The graph of the compound inequality is the
. Find the union by combining the two regions.
4
5
6
7
PTS: 1
DIF: Average
REF: Page 204
OBJ: 3-6.3 Solving Compound Inequalities Involving OR
TOP: 3-6 Solving Compound Inequalities
40. ANS:
OR
17
8
9
10
s
NAT: 12.5.4.a
–10 –9 –8
–7 –6
–5 –4
–3 –2
x –5
The numbers to the left of –5
are shaded.
A solid circle is used.
This part of the inequality
uses 
–1
0
1
2
3
4
5
6
OR
The shaded area is not
between two numbers so
the compound inequality
uses OR.
7
8
9
10 x
x>3
The numbers to the right of 3 are
shaded.
An empty circle is used.
This part of the inequality uses >.
PTS: 1
DIF: Basic
REF: Page 205
OBJ: 3-6.4 Writing a Compound Inequality from a Graph
TOP: 3-6 Solving Compound Inequalities
41. ANS:
2
Test each value to see which is a solution of
AND
NAT: 12.5.4.a
.
If x = 14, then
AND
. The first inequality is false, so the compound inequality is false.
If x = 12, then
AND
. The first inequality is false, so the compound inequality is false.
If x = –6, then
false.
AND
. The second inequality is false, so the compound inequality is
If x = 2, then
AND
. Both inequalities are true, so the compound inequality is true.
PTS: 1
DIF: Advanced
NAT: 12.5.4.c
TOP: 3-6 Solving Compound Inequalities
42. ANS:
A pool is filled with water using one valve. A little time after the pool is filled to its capacity, the pool needs
to be emptied because of some problems. Then, the pool is refilled immediately, using two valves this time.
First, identify the labels. The x-axis is the time, and the y-axis is the water level. Then, analyze the sections of
the graph. Over time, the water level increased steadily, then remained unchanged, next decreased steadily,
then increased steadily, and finally remained unchanged.
PTS: 1
DIF: Average
REF: Page 232
NAT: 12.5.2.b
TOP: 4-1 Graphing Relationships
43. ANS:
x-intercept: 10, y-intercept: 5
The graph intersects the x-axis at (10, 0). The x-intercept is 10.
The graph intersects the y-axis at (0, 5). The y-intercept is 5.
OBJ: 4-1.3 Writing Situations for Graphs
PTS: 1
DIF: Basic
REF: Page 303
OBJ: 5-2.1 Finding Intercepts
NAT: 12.5.1.e
TOP: 5-2 Using Intercepts
KEY: linear equation | x-intercept | y-intercept | intercepts
44. ANS:
x-intercept: –8, y-intercept: 4
To find the x-intercept, replace y with 0 and solve for x; to find the y-intercept, replace x with 0 and solve for
y.
18
x-intercept
y-intercept
PTS: 1
DIF: Average
REF: Page 303
NAT: 12.5.1.e
TOP: 5-2 Using Intercepts
KEY: linear equation | x-intercept | y-intercept | intercepts
45. ANS:
OBJ: 5-2.1 Finding Intercepts
y
36
Number of skirts
30
24
18
12
6
6
12
18
24
30
x
Number of jackets
The x-intercept is (20, 0). The x-intercept gives the total number of jackets that can be made from one bolt of
fabric when only jackets are made.
The y-intercept is (0, 30). The y-intercept gives the total number of skirts that can be made from one bolt of
fabric when only skirts are made.
Find the intercepts by solving the equation for x when y = 0 and for y when x = 0.
Let x = 0.
2.4(0) + 1.6y = 48
(0, 30)
Let y = 0.
2.4x + 1.6(0) = 48
(20, 0)
1.6y = 48
1.6x = 48
y=
x=
y = 30
Use the intercepts to draw the line.
x = 20
The x-intercept is 30. It represents the number of jackets that can be made from a 48-yard bolt of fabric, when
y = 0 and no skirts are made.
The y-intercept is 20. It represents the number of skirts that can be made from a 48-yard bolt of fabric, when x
= 0 and no jackets are made.
PTS: 1
DIF: Average
REF: Page 304
NAT: 12.5.1.e
TOP: 5-2 Using Intercepts
46. ANS:
x-intercept: 2, y-intercept: 3
19
OBJ: 5-2.2 Application
y
10
8
6
4
2
–10 –8 –6
–4 –2
–2
2
4
6
8
x
–4
–6
–8
–10
To find the x-intercept, let y = 0 and solve for x; to find the y-intercept, let x = 0 and solve for y.
Then, plot the intercepts and draw a line connecting them.
PTS:
OBJ:
TOP:
KEY:
47. ANS:
 53
1
DIF: Average
REF: Page 305
5-2.3 Graphing Linear Equations by Using Intercepts
NAT: 12.5.1.e
5-2 Using Intercepts
linear equation | graphing | x-intercept | y-intercept | intercepts
Use the slope formula.
Substitute
for
and
for
.
Simplify.
=3
5
PTS: 1
DIF: Basic
REF: Page 320
OBJ: 5-4.1 Finding Slope by Using the Slope Formula
NAT: 12.5.2.b
TOP: 5-4 The Slope Formula
48. ANS:
The slope is
. The slope means that the amount of money in the account is decreasing at a rate of $50
every week.
In this situation, y represents the amount of money in the account, and x represents the time. So the slope
represents
. The slope of
means that the amount of money in the account is decreasing at a rate of
$50 every week.
PTS: 1
NAT: 12.5.2.c
49. ANS:
DIF: Average
REF: Page 322
TOP: 5-4 The Slope Formula
20
OBJ: 5-4.3 Application
1
3
Find the x-intercept by substituting x = 0 into the equation. Find the y-intercept by substituting y = 0 into the
equation. Use the two intercept points and the slope formula,
PTS: 1
DIF: Average
REF: Page 322
OBJ: 5-4.4 Finding Slope from an Equation
TOP: 5-4 The Slope Formula
50. ANS:
3
y = 2x + 2
, to calculate the slope.
NAT: 12.5.2.c
The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept. Substituting 2 for the
3
3
slope and 2 for the y-intercept gives y = 2x + 2 .
PTS: 1
DIF: Basic
REF: Page 335
OBJ: 5-6.2 Writing Linear Equations in Slope-Intercept Form NAT: 12.5.3.d
TOP: 5-6 Slope-Intercept Form
KEY: slope | y-intercept | slope-intercept form
51. ANS:
y = 4x – 14
If you are given the slope and one point, you can find the y-intercept by substituting for m, x, and y in the
equation y = mx + b. Then, solve for b.
–2 = 4(3) + b
–2 = 12 + b
–14 = b
So, the equation of the line in slope-intercept form is y = 4x – 14.
PTS: 1
DIF: Average
REF: Page 335
OBJ: 5-6.2 Writing Linear Equations in Slope-Intercept Form NAT: 12.5.3.d
TOP: 5-6 Slope-Intercept Form
KEY: slope | y-intercept | slope-intercept form
52. ANS:
y
10
8
6
4
2
–10 –8 –6
–4 –2
–2
2
4
6
8
x
–4
–6
–8
–10
21
,
Plot
. Count 1 down and 2 right, and plot another point. Draw a line connecting the two points.
y
10
8
6
4
2
–10 –8
–6
–4
–2
–2
–4
2
4
6
8
10
x
(0, –3)
(2, –4)
–6
–8
–10
PTS: 1
DIF: Average
REF: Page 336
OBJ: 5-6.3 Using Slope-Intercept Form to Graph
TOP: 5-6 Slope-Intercept Form
53. ANS:
NAT: 12.5.3.d
The slope is
, and this is the rate at which the water level is receding. The y-intercept is 34, and this is the
water level after 0 days. In 16 days, the water level will be 26 feet.
Step 1: Write an equation that represents the water level, w, after d days.
Water level
is
receding at 0.5 foot
per day
starting at
34 feet
w
=
d
+
34
An equation is
.
Step 2: Identify the slope and y-intercept and describe their meanings.
The slope is
. This is the rate at which the water level is receding: 0.5 foot per day. The y-intercept is 34.
This is the water level after 0 days, or the starting water level of 34 feet.
Step 3:
Substitute 26 for w in the equation.
Solve for d.
In 16 days, the water level will be 26 feet.
PTS: 1
NAT: 12.5.3.d
54. ANS:
DIF: Average
REF: Page 337
TOP: 5-6 Slope-Intercept Form
22
OBJ: 5-6.4 Application
y
10
8
6
4
2
–10 –8 –6
–4 –2
–2
2
4
6
8
x
–4
–6
–8
–10
To graph the line, plot the given point (3, –7). Then, use the slope
2
3
to plot additional points. Use a rise of 2
(moving up if the slope is positive and down if the slope is negative) and a run of 3 (moving right if positive
and left if negative) to find additional points.
PTS: 1
DIF: Basic
REF: Page 341
OBJ: 5-7.1 Using Slope and a Point to Graph
NAT: 12.5.3.d
TOP: 5-7 Point-Slope Form
KEY: coordinate plane | graph | point | slope | linear equation
55. ANS:
y + 7 = 6(x + 8)
Substitute the point and slope into the point-slope form
, where m represents the slope and
represents a point on the line.
PTS: 1
DIF: Average
REF: Page 342
OBJ: 5-7.2 Writing Linear Equations in Point-Slope Form
NAT: 12.5.3.d
TOP: 5-7 Point-Slope Form
KEY: linear equation | point-slope form
56. ANS:
x + 5
First, write the equation in point-slope form.

Next, solve the equation for y.

x + 2
x + 5
PTS: 1
DIF: Basic
REF: Page 342
OBJ: 5-7.3 Writing Linear Equations in Slope-Intercept Form
TOP: 5-7 Point-Slope Form
57. ANS:
3
37
y=4x+ 4
23
NAT: 12.5.3.d
Calculate the slope of the line through the two points by using the equation
. Then substitute that
value along with the coordinates of one of the given points into the equation
to find b.
PTS: 1
DIF: Average
REF: Page 343
OBJ: 5-7.4 Using Two Points to Write an Equation
NAT: 12.5.2.c
TOP: 5-7 Point-Slope Form
KEY: linear equation | slope-intercept form
58. ANS:
; Cost for truck = $40.15
Use any two points to find the slope.
To find an equation, substitute the slope and any ordered pair from the table into the point-slope form. Then
solve for y to put the equation into slope-intercept form.
To find the cost for the truck, substitute the truck’s tank size for x and simplify.
y = 1.70x + 2.75
y = 1.70(22) + 2.75
y = 40.15
The cost for the truck is $40.15.
PTS: 1
NAT: 12.5.4.c
59. ANS:
DIF: Average
REF: Page 343
TOP: 5-7 Point-Slope Form
OBJ: 5-7.5 Problem-Solving Application
Step 1 Find the y-intercept.
Subtract x from both sides.
Divide both sides by 4.
Step 2 Find the slope.
Use the slope formula.
Substitute the given point
and simplify.
PTS: 1
DIF: Advanced
and the
TOP: 5-7 Point-Slope Form
24