Algebra 1 Midterm Worksheet
Short Answer
1. Salvador has saved 130 sand dollars and wants to give them away equally to n friends. Write an
expression to show how many sand dollars each of Salvador’s friends will receive. Then, find the
total number of sand dollars each of Salvador’s friends will get if Salvador gives them to 10 friends.
2. Isabel reads 15 books from the library each month for y months in a row. Write an expression to
show how many books Isabel read in all. Then, find the number of books Isabel read if she read for
12 months.
3. Divide.
4. Simplify
.
5. Write all classifications that apply to the real number
.
6. Translate the word phrase, the product of 8.5 and the difference of –4 and –8, into a numerical
expression.
7. A phone company advertises a new plan in which the customer pays a fixed amount of $25 per month
for unlimited calls in the country, and $0.10 per minute for international calls. Find a rule for the
monthly payment a customer pays according to the new plan. Write ordered pairs for the monthly
payment when the customer uses 90, 120, 145, and 150 international minutes in a month.
8. The coordinates of three vertices of a rectangle are
,
, and
coordinates of the fourth vertex. Then, find the area of the rectangle.
. Find the
9. Solve –14 + s = 32.
10. Solve
11. Solve
. Check your answer.
.
12. Devon pays $39.95 for her hair color analysis. After that she pays $4.95 for each color touchup.
What is the greatest number of touchups she can afford if the total amount she spends cannot be
more than $84.50?
13. The formula
gives the profit p when a number of items n are each sold at a cost c and
expenses e are subtracted. If
,
, and
, what is the value of c?
14. A video store charges a monthly membership fee of $7.50, but the charge to rent each movie is only
$1.00 per movie. Another store has no membership fee, but it costs $2.50 to rent each movie. How
many movies need to be rented each month for the total fees to be the same from either company?
15. Solve
16. Solve
for x.
.
17. Solve
.
18. On a sunny day, a 5-foot red kangaroo casts a shadow that is 7 feet long. The shadow of a nearby
eucalyptus tree is 35 feet long. Write and solve a proportion to find the height of the tree.
19. A right triangle has legs 15 inches and 12 inches. Every dimension is multiplied by
to form a new
right triangle with legs 5 inches and 4 inches. How is the ratio of the areas related to the ratio of
corresponding sides?
20. What percent of 74 is 481? If necessary, round your answer to the nearest tenth of a percent.
21. Find the result when 28 is decreased by 25%.
22. 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.
23. Sam earned $450 during winter vacation. He needs to save $180 for a camping trip over spring
break. He can spend the remainder of the money on music. Write an inequality to show how much he
can spend on music. Then, graph the inequality.
24. Solve the inequality
2 and graph the solutions.
25. 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?
26. Solve the inequality z + 8  3 z
–4 and graph the solutions.
27. Solve
.
28. Fly with Us owns a D.C.10 airplane that has seats for 240 people. The company flies this airplane only
if there are at least 100 people on the plane. Write a compound inequality to show the possible
number of people in a flight on a D.C.10 with Fly with Us. Let n represent the possible number of
people in the flight. Graph the solutions.
29. Graph the solution of
AND
?
30. Solve the inequality.
31. Solve the inequality.
32. Express the relation for the math test scoring system {(1, 2), (2, 3), (3, 5), (4, 10), (5, 5)} as a table,
a graph and a mapping diagram.
33. Identify the independent and dependent variables in the situation.
As Kyoko works more hours, her total pay increases.
34. For
, find
35. Graph the function
36. Graph the function
when x = –1.
.
.
37. The function
describes how far from home Shu Ling is as she drives from Dallas to Miami.
Graph the function. Use the graph to estimate how far from home Shu Ling is in 12 hours.
38. Graph a scatter plot using the given data. Describe the correlation.
x
y
3
4.5
6
6.5
5
6.5
2
3.5
7
6.5
4
4.5
8
8
1
4
39. Julio is training for a swimming race. The first part of his training schedule is shown.
Session
Swimming distance
(mi)
1
0.25
2
0.55
3
0.85
4
1.15
5
1.45
6
1.75
Is this training schedule an arithmetic sequence? Explain. If Julio’s training schedule starts on a
Tuesday and he swims every two days, on which day will he swim for 2.95 miles?
40. Identify whether each graph represents a function. If the graph does represent a function, is the
function linear?
Graph A
Graph B
Graph C
y
y
y
3
5
3
2
4
2
1
3
1
2
–3
–2
–1
–1
1
2
3 x
–2
1
–2
–1
–1
1
2
3
4 x
–2
–1
–3
–1
1
x
–3
41. Find the x- and y-intercepts.
y
10
8
6
4
2
–10 –8
–6
–4
–2
–2
2
4
6
8
10
x
–4
–6
–8
–10
42. Jim drove for several hours, recording the distance he had traveled in miles. Graph the data and
show the rates of change.
Hours
Miles
1
50
4
220
6
300
7
320
10
500
43. Find the slope of the line.
y
10
8
6
(–4, 3)4
(6, 3)
2
–10 –8
–6
–4
–2
–2
2
4
6
8
10
x
–4
–6
–8
–10
44. The graph shows a linear relationship. Find the slope.
y
10
8
6
4
2
–10 –8
–6
–4
–2
–2
(1,
2 –1)
4
6
8
10
x
–4
–6
(7, –8)
–8
–10
45. 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)
46. M is the midpoint of
coordinates of Q?
. P has coordinates (–1, 5) and M has coordinates (–3, 2). What are the
47. Tell whether the equation
variation.
represents a direct variation. If so, identify the constant of
48. Tell whether the relation is a direct variation. Explain.
x
y
–10
20
–9
18
1
–2
49. The value of y varies directly with x, and y = 27 when x = 18. Find y when x = 36.
50. Write the equation that describes the line with slope = 2 and y-intercept =
3
2
in slope-intercept
form.
51. Write an equation in point-slope form for the line that has a slope of 6 and contains the point (–8,
–7).
52. Write an equation in slope-intercept form of the line with slope  2 that contains the point
1
(–4, –3).
53. Write an equation in slope-intercept form for the line parallel to y = 5 x – 2 that passes through (8,
–2).
54. Describe the transformation from the graph of
55. Graph
. Then reflect the graph of
describe the new graph.
to the graph of g(x) =
1
4
x.
across the x-axis. Write a function
to
56. Graph the absolute-value function, f(x) = |x – 3|.
57. Find the 52nd term of the arithmetic sequence with a1 = -1 and d = -7
58. Find the distance between (2, 7) amd (-4, 12).
59. Steve rides his bike 15 miles per hour.Convert this to feet per second..
60. Eileen bought a backpack for $32. The wholesale cost was $20. What was the percent markup?
Algebra 1 Midterm Worksheet
Answer Section
SHORT ANSWER
1. ANS:
; 13 sand dollars
The expression
Evaluate
models the number of sand dollars each of Salvador’s friends will receive.
for n = 10.
= 13
If Salvador gives 130 sand dollars to 10 friends, each friend will get 13 sand dollars.
PTS: 1
NAT: 8.5.3.b | 12.5.3.b | 12.5.3.e
KEY: algebraic expression | word problem | operation
2. ANS:
15y; 180 books
The expression 15y models the number books Isabel read in all.
Evaluate 15y for y = 12.
15(12) = 180
If Isabel read for 12 months, then that means Isabel read 180 books.
PTS: 1
NAT: 8.5.3.b | 12.5.3.b | 12.5.3.e
KEY: algebraic expression | word problem | operation
3. ANS:
8
8 21
Write
as an improper fraction.
To divide by
multiply by
.
Multiply.
8
8 21
PTS: 1
Simplify.
NAT: 8.1.3.a | 12.1.3.b
4. ANS:
25
36
The exponent tells how many times to multiply the fraction by itself.
Multiply
PTS: 1
by itself 2 times.
NAT: 8.1.3.a | 12.1.3.a
KEY: power | exponent | fraction
5. ANS:
rational number, terminating decimal, integer, whole number, natural number
Any number that can be written as a fraction is a rational number. Rational numbers include
terminating decimals and repeating decimals.
If a rational number simplifies to a whole number or its opposite, it is also an integer.
If a rational number simplifies to a nonzero whole number, it is also a natural number.
PTS: 1
NAT: 12.1.5.f
KEY: real number | classify | rational | irrational
6. ANS:
Use parentheses so that the difference is
evaluated first.
Product means multiplication.
PTS: 1
NAT: 12.1.5.e
7. ANS:
; (90, 34), (120, 37), (145, 39.5), (150, 40)
Let y represent the monthly payment and x represent the number of minutes of international calls.
monthly
is
$25
plus
$0.10 for each
international
payment
minute
y
x
=
25
+
0.10
Number of
international minutes
x (input)
90
120
145
150
PTS: 1
8. ANS:
NAT: 8.5.2.d
; Area = 72 square units
Step 1 Plot the points.
Rule
Monthly
payment
y (output)
$34.00
$37.00
$39.50
$40.00
Ordered pair
(x, y)
(90, 34)
(120, 37)
(145, 39.5)
(150, 40)
y
5
4
B
3
C
2
1
1
–1
2
3
4
5
6
7
8
9
10
x
–2
–3
–4
–5
A
Step 2 Find the fourth vertex.
The fourth vertex will have the same x-coordinate as C(10,3) and the same y-coordinate as A(1, –5).
x-coordinate: 10
y-coordinate: –5
The fourth vertex is D(10, –5).
y
5
4
3
B
C
2
1
1
–1
2
3
4
5
6
7
8
9
10
x
–2
–3
–4
–5
A
D
Step 3 Find the area of the rectangle.
square units
PTS: 1
NAT: 8.3.4.d | 12.3.4.d
KEY: multi-step
9. ANS:
s = 46
When something is added to the variable, add its opposite to both sides of the equation to isolate
the variable. Here, –14 is added to the variable, so add 14 to both sides of the equation to isolate s.
PTS: 1
10. ANS:
q = 205
NAT: 8.5.4.a | 12.5.4.a
KEY: equations | solving | subtraction
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
NAT: 8.5.4.a | 12.5.4.a
KEY: equation | multiplication | solving
11. ANS:
Since
is subtracted from
, add
to both sides
to undo the subtraction.
Since f is divided by 45, multiply both sides by 45 to
undo the division.
Simplify.
PTS: 1
NAT: 12.5.4.a
KEY: equations | two-step | multi-step
12. ANS:
9
After paying $39.95 for a hair color analysis, the number of color touchups that Devon can afford is
.
PTS: 1
NAT: 8.5.4.c | 12.5.4.c
KEY: multi-step | equations
13. ANS:
1.55
Substitute 3750 for p, 3000 for n, and 900 for e.
Add 900 to both sides of the equation.
Divide both sides by 3000.
PTS: 1
14. ANS:
NAT: 8.5.4.a | 12.5.4.a
KEY: equation | two-step | multi-step
5 movies
Let m represent the number of movies rented each month.
Here are the costs for each company (in dollars).
7.5 + m
2.5m
=
To collect the variable terms on one side, subtract m from both sides.
7.5 – m
2.5m – m
=
1.5 m
7.5
=
Divide both sides by 1.5.
m
=
5
m
=
PTS: 1
NAT: 8.5.4.c | 12.5.4.c
KEY: equation | solving | variables on both sides
15. ANS:
Add z to both sides.
Divide both sides by 4.
PTS: 1
NAT: 12.5.4.f
16. ANS:
x = 13 or x = –1
KEY: literal equation | solving for a variable
Divide both sides by 7.
What numbers are 7 units from 0?
Case 1:
x–6=7
PTS: 1
Case 2:
x – 6 = –7
Rewrite the equation as two cases.
The solutions are x = 13 or x = –1.
NAT: 12.5.4.a
KEY: absolute value | equation
17. ANS:
No solution
First, isolate the absolute value expression.
Subtract 8 from both sides.
The absolute value expression is equal to a negative number, which is impossible. The equation has no
solution.
PTS: 1
NAT: 12.5.4.a
KEY: absolute value | equation
18. ANS:
; 25 feet
Use cross products.
Since x is multiplied by 7, divide both sides by 7 to undo
the multiplication.
The tree is 25 feet tall.
PTS: 1
NAT: 12.2.1.b
KEY: equivalent ratios | equivalent rates | multiplication and division of whole numbers | proportions
19. ANS:
The ratio of the areas is the square of the ratio of the corresponding sides.
Find the areas of the two right triangles:
,
Then, find the ratio of the sides and the ratio of the corresponding areas.
ratio of the sides:
ratio of the areas:
The ratio of the areas is the square of the ratio of the corresponding sides.
PTS: 1
NAT: 8.2.1.f | 12.2.1.f
KEY: ratio | proportion | scale
20. ANS:
650%
Method 1 Use a proportion.
Use the percent proportion.
Let x represent the percent.
Find the cross products.
Since x is multiplied by 74, divide both sides by 74 to
undo the multiplication.
_481 is 650% of 74.
Method 2 Use an equation.
Write an equation. Let x represent the percent.
Since x is multiplied by 74, divide both sides by 74 to
undo the multiplication.
The answer is a decimal.
Write the decimal as a percent.
_481 is 650% of 74.
PTS: 1
NAT: 8.1.4.d | 12.1.4.d
KEY: percent
21. ANS:
21
To find the amount of decrease, multiply 28 by 0.25. Then, subtract the decrease from 28 to find
the result of the decrease.
PTS: 1
NAT: 8.1.4.d | 12.1.4.d
KEY: percent | increase | decrease
22. 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
NAT: 8.1.4.d | 12.1.4.d
KEY: percent change | percent decrease | percent increase
23. ANS:
;
s
–500
–400
–300
–200
–100
0
100
200
300
400
500
Sam has $450, but must save $180 of that for his camping trip.
If s is the amount he can spend on music, then
.
So,
.
s
–500
–400
–300
–200
PTS: 1
–100
0
100
200
300
NAT: 8.5.4.c | 12.5.4.c
400
500
KEY: inequalities | graph | number line
24. ANS:
z –8
–10 –8
–6
–4
–2
0
2
4
6
8
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
when the value is not included, such as with > or <.
–10 –8
–6
–4
–2
0
2
4
6
8
or
Use an empty circle
10
PTS: 1
NAT: 8.5.4.a | 12.5.4.a
KEY: inequality | solving | multiplication | division
25. ANS:
5 tickets
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: 8.5.4.c | 12.5.4.c
KEY: inequalities | solving | multiplying | dividing
26. ANS:
z –3
–10 –8
–6
–4
–2
0
2
z + 8  3 z –4
4z + 8 –4
4z –12
z
–6
–4
–2
6
8
10
Combine like terms.
Subtract 8 from both sides.
Divide both sides by 4. When you divide by a negative
number, reverse the inequality symbol. When you divide by
a positive number, keep the same inequality symbol.
–3
–10 –8
4
0
2
4
6
8
10
Use a solid circle when the value is included in the graph, such as with
when the value is not included, such as with > or <.
PTS: 1
NAT: 8.5.4.a | 12.5.4.a
or
Use an empty circle
KEY: multistep inequality | solving
27. ANS:
Combine like terms.
Simplify.
Divide both sides by 0.5.
PTS: 1
NAT: 8.5.4.a | 12.5.4.a
KEY: inequalities | variables on both sides
28. ANS:
–250
–200
–150
–100
–50
0
50
100
150
200
Let n represent the possible number of people in the flight.
n
100
is less than or equal
is less than or equal
to
to
n
100
–250
–200
PTS: 1
–150
–100
–50
0
50
NAT: 8.5.4.c | 12.5.4.c
29. ANS:
2
Test each value to see which is a solution of
100
150
250
240
240
200
250
KEY: inequalities | compound
AND
.
If x = 14, then
false.
AND
. The first inequality is false, so the compound inequality is
If x = 12, then
false.
AND
. The first inequality is false, so the compound inequality is
If x = –6, then
is false.
AND
. The second inequality is false, so the compound inequality
If x = 2, then
PTS: 1
30. ANS:
AND
. Both inequalities are true, so the compound inequality is true.
NAT: 8.5.4.a | 12.5.4.a
KEY: inequalities | compound
The solution set is all real numbers.
Subtract 9 from both sides.
Absolute-value expressions are always nonnegative.
Therefore, the statement is true for all values of x.
The solution set is all real numbers.
PTS: 1
NAT: 8.5.4.a | 12.5.4.a
KEY: inequality | absolute
31. ANS:
The solution set is all real numbers.
Subtract 9 from both sides.
Absolute-value expressions are always nonnegative.
Therefore, the statement is true for all values of x.
The solution set is all real numbers.
PTS: 1
NAT: 8.5.4.a | 12.5.4.a
KEY: inequality | absolute
32. ANS:
10
9
8
Point value
7
6
5
4
3
2
1
1
2
3
4
5
Problem
The domain is the set of first elements (or x-coordinates) of the ordered pairs. The range is the set
of second elements (or y-coordinates) of the ordered pairs.
PTS: 1
NAT: 8.5.1.e | 12.5.1.e
KEY: relation | function | multiple representations
33. ANS:
Independent: hours worked; Dependent: total pay
The value of the dependent variable depends on the value of the independent variable.
In this situation, the total amount Kyoko is paid depends on the number of hours she works, so hours
worked is the independent variable and total pay is the dependent variable.
PTS: 1
NAT: 8.5.2.b | 12.5.2.b
KEY: independent variable | dependent variable
34. ANS:
6
Substitute –1 for x.
Simplify.
PTS: 1
NAT: 12.5.3.f
KEY: function | input | output | evaluate
35. ANS:
y
6
5
4
3
2
1
–6 –5 –4 –3 –2 –1–1
1
2
3
4
5
6
x
–2
–3
–4
–5
–6
Step 1: Choose several values of x and generate ordered pairs.
x
y
–3
0
–1
1
1
2
3
y
Step 2: Plot enough points to see a
pattern.
Step 3: Draw a line through all the
points to show all the ordered pairs
that satisfy the function.
6
5
4
3
2
1
–6 –5 –4 –3 –2 –1–1
–2
–3
–4
–5
–6
1
2
3
4
5
6
x
PTS: 1
NAT: 8.5.4.d | 12.5.4.c
KEY: graph | function
36. ANS:
y
6
5
4
3
2
1
–6 –5 –4 –3 –2 –1
–1
1
2
3
4
5
6 x
–2
–3
–4
–5
–6
Step 1: Choose several values of x and generate ordered pairs.
x
y
–6
–3
0
–2
1
–3
2
–6
y
Step 2: Plot enough points to see a
pattern.
Step 3: Draw a curve through all the
points to show all the ordered pairs
that satisfy the function.
6
5
4
3
2
1
–6 –5 –4 –3 –2 –1–1
–2
–3
–4
–5
–6
PTS: 1
37. ANS:
NAT: 12.5.4.c
KEY: graph | function
1
2
3
4
5
6
x
y
2000
1800
1600
Miles
1400
1200
1000
800
600
400
200
4
8
12
16
20
24
28
x
32
Hours
Shu Ling is about 480 miles from home in 12 hours.
Create a table to find points that should be included on the graph. Only use positive values because
distance cannot be negative.
x
y
0
0
10
400
20
800
30
1200
Graph the points and connect with a line.
y
2000
1800
1600
Miles
1400
1200
(30, 1200)
1000
800
(20, 800)
600
400
(10, 400)
200
(0, 0)
4
8
12
16
20
24
28
32
36
40
44
48
x
Hours
PTS: 1
NAT: 8.5.4.c | 12.5.4.c
KEY: function | graph | rate | time | distance | speed
38. ANS:
y
10
9
8
7
6
5
4
3
2
1
1
2
3
4
5
6
7
x
8
Use the table to make ordered pairs. Plot the ordered pairs to make a scatter plot.
PTS: 1
NAT: 8.4.1.b | 12.4.1.b
KEY: line of best fit | scatter plot
39. ANS:
Julio’s training schedule is an arithmetic sequence, because a constant increase of 0.3 occurs
between the sessions. Julio will swim 2.95 miles on Saturday.
According to Julio’s training schedule, he increases his swimming distance by 0.3 miles each time.
This is an arithmetic sequence.
Write the rule for an arithmetic sequence.
Substitute 0.3 for d, 0.25 for
, and 2.95 for
.
Simplify and solve.
On the 10th session, Julio will swim 2.95 miles. Because he begins on Tuesday and swims every other
day, his 10th session will occur on a Saturday.
PTS: 1
NAT: 8.5.1.a | 12.5.1.e
KEY: arithmetic sequence
40. ANS:
Graph A: not a linear function
Graph B: linear function
Graph C: not a function
In a function, each domain value is paired with exactly one range value.
Graph A is a function, but it is not linear.
Graph B is a function and a line.
Graph C is not a function because each domain value (2.8) pairs with infinite range values.
PTS: 1
NAT: 8.5.1.e | 12.5.1.e
KEY: function | linear | identify
41. 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.
PTS: 1
NAT: 8.5.1.f | 12.5.1.e
KEY: linear equation | x-intercept | y-intercept | intercepts
42. ANS:
y
3
500
180
450
60
400
350
Miles
1
20
2 20
300
80
250
3
200
170
40
150
56.67
100
50
1
2
3
4
5
6
7
8
x
9
Hours
Hours are the independent variable and should be placed along the horizontal axis with a scale that
ranges from 1 to 10. Miles are the dependent variable and should be placed on the vertical axis with
a scale that ranges from 50 to 500. This leaves only two answer choices as options.
The rate is not constant, as
does not equal
, so a straight line should not occur, eliminating
the choice where the line is straight.
PTS: 1
NAT: 8.5.2.b | 8.5.4.d | 12.5.2.b
KEY: slope | rate of change
43. ANS:
0
. The slope is 0.
PTS: 1
NAT: 8.5.2.b | 12.5.2.b
KEY: slope | rate of change
44. ANS:
6
7
Use the slope formula.
Substitute
= 6
7
PTS: 1
45. ANS:
for
and
for
.
Simplify.
NAT: 8.5.4.d | 12.5.2.a
KEY: slope formula | linear | graph
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: 8.5.4.d | 12.5.2.b
KEY: slope formula | application | graph
46. ANS:
(–5, –1)
Use the Midpoint Formula. Substitute the values for the midpoint you have and solve for the x- and
y-values of point Q.
PTS: 1
NAT: 8.3.4.a | 12.3.4.a
KEY: midpoint | graph
47. ANS:
Not a direct variation.
An equation is a direct variation if it can be written in the form y = kx, where k is the constant of
variation.
y=
1
4
x–2
This is not a direct variation, because it cannot be written in the form y = kx.
PTS: 1
variation
NAT: 8.5.2.b | 12.5.2.b
KEY: direct variation | constant of
48. ANS:
This is a direct variation, because it can be written as
, where k = –2.
Write an equation in the form
where k is the constant of variation.
Find
for each ordered pair.
;
;
This is a direct variation, because
is the same for each ordered pair. –2 is the constant of
variation.
PTS: 1
NAT: 8.5.2.b | 12.5.2.b
49. ANS:
y = 54
Set up a proportion.
KEY: direct variation | function
Substitute 36 for x.
(18)y = 36(27)
18y = 972
Cross multiply.
Divide both sides by 18.
y = 54
PTS: 1
NAT: 12.5.3.f
KEY: direct variation | function | evaluate
50. ANS:
y = 2x +
3
2
The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept. Substituting
2 for the slope and
PTS: 1
form
3
2
for the y-intercept gives y = 2 x +
NAT: 8.5.3.b | 12.5.3.b
3
2
.
KEY: slope | y-intercept | slope-intercept
51. ANS:
y + 7 = 6 (x + 8)
Substitute the point and slope into the point-slope form
slope and
, where m represents the
represents a point on the line.
PTS: 1
NAT: 8.5.3.b | 12.5.3.b
KEY: linear equation | point-slope form
52. ANS:
2 x – 5
1
First, write the equation in point-slope form.
2
1
Next, solve the equation for y.
2
1
2 x – 2
1
2 x – 5
1
PTS: 1
NAT: 8.5.3.b | 12.5.3.b
KEY: slope | intercept | equation
53. ANS:
y = 5 x – 42
Parallel lines have the same slope.
Since the given line has a slope of 5 , the parallel line has a slope of 5 .
y – y1 = m(x – x1)
y – (–2) = 5 (x – (8))
Use the point-slope form to write an equation.
Substitute 5 for m and (8, –2) for (x1, y1).
y = 5 x – 42
Distribute 5 on the right side. Add –2 to both sides.
PTS: 1
NAT: 8.3.4.a | 12.3.4.a
KEY: slope | parallel | perpendicular | intercept | point | equation
54. ANS:
The graph of g(x) =
1
4
x is the result of rotating the graph of
clockwise.
The graph of g(x) is less steep than the graph of f(x).
The graph of g(x) =
y
4
x is the result of
rotating the graph of
clockwise. The graph of g(x) is less
steep than the graph of f(x).
3
f(x)
2
1
4
1
g(x)
–4
–3
–2
–1
1
2
3
4
x
–1
–2
–3
–4
PTS: 1
NAT: 12.5.2.d
KEY: transformation | rotation | linear | function | graph
55. ANS:
y
5
g(x)
4
3
2
1
–4
–3
–2
–1
–1
1
2
3
4
x
–2
–3
–4
f(x)
–5
To find
, multiply m by
. In
, m = –4. So
.
y
5
g(x)
4
3
2
1
–5
–4
–3
–2
–1
–1
1
2
3
4
x
5
–2
–3
–4
f(x)
–5
PTS: 1
NAT: 12.5.2.d
56. ANS:
The domain is all real numbers.
y
5
Axis of
4
symmetry
3
KEY: transformation | reflection | linear | function | graph
(0, 3)
2
1
(3, 0)
–5
–4
–3
–2
–1
–1
1
2
3
4
x
5
x=3
–2
–3
–4
–5
The range is y
0.
Make a table of positive, negative, and
zero values for x to find ordered pairs.
Graph the ordered pairs and connect
with a straight line.
y
(–1, 4)
5
Axis of
4
symmetry
3
(0, 3)
1
–5
–4
–3
–2
–1
–1
(3, 0)
1
2
3
4
–2
–3
–4
–5
Get information from the graph.
(5, 2)
2
x=3
(–2, 5)
5
x
The axis of symmetry is x = 3.
The vertex is (3, 0).
The x-intercept is 3.
The y-intercept is 3.
The domain is all real numbers.
The range is y 0.
PTS: 1
NAT: 8.5.2.b | 12.5.1.i | 12.5.2.b
KEY: absolute value | graph | intercepts | domain | range
57. ANS:
-358
PTS: 1
58. ANS:
square root of 61
PTS: 1
59. ANS:
22 feet per second
PTS: 1
60. ANS:
60% markup
PTS: 1