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2-Variable Relationships and 2-step equations

Total questions: 115

Worksheet time: 19hrs 23mins

Name
Class
Date
1.
What is the constant of proportionality? 
a)
5
b)
1/5
c)
10
d)
2
2.
What is the constant of proportionality? 
a)
6
b)
3
c)
2
d)
1/2
3.
What is the constant of proportionality of the relationship represented by the table above?
a)
75
b)
0.013
c)
1/75
d)
None of the above
4.
What is the constant of proportionality for the table above?
a)
2
b)
1/2
c)
3
d)
None of the above
5.

Determine the constant of proportionality for the table. Express your answer as y = kx

a)

y = 1/2x

b)

x = 1/2y

c)

y = 2x

d)

k = x

6.

Determine the constant of proportionality for the table. Express your answer as y = kx

a)

y = 30k

b)

y = 30x

c)

y = 0.03x

d)

y = 9x

7.
Is the given table a proportional relationship? If so, what is the constant?
a)
Yes; 1/3
b)
Yes; 3
c)
Yes; 5
d)
No
8.
Write the equation for the table given.
a)
y = 16x
b)
y=8x
c)
y=12x
9.

What is the constant of proportionality for this table?

a)

$1/9 per hour

b)

$9 per hour

c)

$8 per hour

d)

$18 per hour

10.
What is the constant of proportionality for the following graph?
a)
80
b)
20
c)
40
d)
160
11.

Does this graph show a proportional relationship?

a)

Yes

b)

No

12.

What makes a graph proportional?

a)

Linear (straight line), that does NOT go through the origin.

b)

A straight line (linear) that goes through the origin

13.

Does this graph show a proportional relationship?

a)

Yes

b)

No

c)

Sometimes

14.

Which tables and graphs show a proportional relationship?

a)

A,C,F

b)

B,D,E

c)

B,C,F

d)

A,B,D

15.

Albert wants to buy some pens. He compares 4 different packs of pens. Which two packs of pens have the same cost per pen?

a)

Packs 1 and 2

b)

Packs 1 and 3

c)

Packs 2 and 4

d)

Packs 1 and 4

16.

The graph shows the distance a train travels over time. How fast is the train traveling?

a)

25 miles per hour

b)

90 miles per hour

c)

50 miles per hour

d)

45 miles per hour

17.

Use the table to write an equation that relates lunch cost L and number of riders n.

a)

L = $0.50n

b)

L = $4.00n

c)

L = $6.00n

d)

L = $8.00n

18.
The constant of proportionality can be found by finding the __________  _____________.
a)
unit rate
b)
ratio rate
c)
proportion answer
d)
rational number
19.

Find the Constant Rate of Change of 624 calories in 3 servings.

a)

1,872 calories per serving

b)

208 calories per serving

c)

624 calories per serving

d)

621 calories per serving

20.
a)
40 CALORIES PER MIN.
b)
15 CALORIES PER MIN.
c)
4 CALORIES PER MIN.
d)
60 CALORIES PER MIN.
21.
a)
9 players per team
b)
12 players per team
c)
10 players per team
d)
11 players per team
22.

What is the constant rate of change?

a)

Not here.

b)

$80 per month.

c)

$82 per month.

d)

$41 per month.

23.

What is the constant rate of change between the quantities in the table?

a)

$1 per hour

b)

$40 per hour

c)

$5 per hour

d)

$10 per hour

24.

Find the constant rate of change for this graph.

a)

2 lb per person

b)

1 lb per person

c)

3 lb per person

d)

4 lb per person

25.

Determine the constant rate of change.

a)

15

b)

6

c)

1/6

d)

-6

26.
You spend $40 on 5 pounds of concrete. What is the unit rate in dollars per pound?
a)
$8 per pound
b)
$5 per pound
c)
$35 per pound
d)
0.125 pounds per dollar
27.

$279 for 9 concert tickets. Find the cost per ticket.

a)

$31

b)

$39

c)

$2,511

d)

$34

28.

If Antonia can type 408 words in 4 minutes, how many words can she type per minute?

a)

408 words per minute

b)

100 words per minute

c)

400 words per minute

d)

102 words per minute

29.
Which is the better deal?
Oreos
$2.98 for 15 oz
OR
Chips Ahoy
$2.50 for 14 oz
a)
Oreos
b)
Chips Ahoy
30.
Which equation matches the table?
a)
y = x + 5
b)
y = 5x
c)
y = x - 5
d)
x = y - 5
31.

Nancy can type 50 words per minute. Look at the table below to write an equation that matches the data.

a)

m=50 + w

b)

w= 50m

c)

w= 50 + m

d)

m= 50 - w

32.

Look at the table below. Write an equation to match the pattern between m, minutes and bubbles blown, b.

a)

b = 12m

b)

b= m +12

c)

b = m ÷ 12

d)

none of these

33.

What is the missing value of the table based on patterns?

a)

25

b)

50

c)

75

d)

27

34.

What equation represents the relationship between the variables in the table?

a)

d = 10t

b)

d = t - 9

c)

d = 10 - t

d)

d = t + 10

35.

What equation matches the table?

a)

y=6x

b)

y=x+10

c)

y=x -10

d)

y=x ÷ 6

36.

What is the independent variable?

The number of students in a class, s, and the number of desks needed, d

a)

number of students in a class, s

b)

number of desks needed, d

c)

number of desks in a class, d

d)

number of students needed, s

37.

What is the independent variable?

The number of candles on a birthday cake, c, and that person's age, a

a)

number of candles on a birthday cake, c

b)

that person's age, a

38.

What is the independent variable?

The height of a sunflower in inches, h, and the number of days since it was planted, p

a)

number of days the sunflower grows, g

b)

number of days since the sunflower was planted, p

c)

height of a sunflower in inches, h

39.

What is the dependent variable?

The height of a sunflower in inches, h, and the number of days since it was planted, p

a)

number of days the sunflower grows, g

b)

number of days since the sunflower was planted, p

c)

height of a sunflower in inches, h

40.

What is the dependent variable?

The number of gallons of paint needed, g, and the size of a room in square feet, s

a)

number of gallons of paint needed, g

b)

the size of the room in square feet, s

41.
Which label best describes the dependent quantities shown in the table?
a)
Number of tickets (t)
b)
Cost (c)
42.
Which label best describes the independent quantities shown in the table?
a)
Number of tickets (t)
b)
Cost (c)
43.
a)
the independent variable is distance
b)
the independent variable is d=25 t
c)
the dependent variable is time
d)
the dependent variable is distance
44.

Emma gets one sticker for every paper she completes.


s = stickers earned

p = papers completed


The independent variable is:

a)

s = stickers earned

b)

p = papers completed

45.

Ms. Shi is making a scrapbook. As she adds more photos, the scrapbook grows thicker.


p = the number of photos added

t = the thickness of the scrapbook

a)

t is the independent variable and p is the dependent variable

b)

p is the independent variable and t is the dependent variable

46.
Sam wanted to know if the color of the chair you sat in when taking a test affected your test grade. What is the independent variable.
a)
Color or chair
b)
Grade on test
c)
Age of students
47.

HYPOTHESIS: Does study time affect the student's score on an test?

Suppose you collected this data from students in your school. What is the independent variable in the study?

a)

The Students

b)

The Study Time

c)

The Grade on the Quiz

48.
A student wants to test the effects of different types of exercise on heart rate.  What is the dependent variable?
a)
heart rate
b)
type of exercise
c)
amount of exercise
d)
time of day exercise occurs
49.
What is the independent variable?
a)
cost of mowing
b)
Moe's Mowing Service
c)
$18
d)
Mowing Time
50.

The total number of markers, m, contained in p packages can be represented by the equation m = 8p. Which of the following tables best represents this situation?

a)
b)
c)
d)
51.

Does the graph represent an additive or multiplicative relationship?

a)

Additive

b)

Multiplicative

c)

Both

d)

Neither

52.

Does the graph represent an additive or multiplicative relationship?

a)

Additive

b)

Multiplicative

c)

Both

d)

Neither

53.

The table shows how many points Joaquin and Jerome scored during 4 basketball games. Which best describes the pattern shown in the table?

a)

It is an additive pattern because the point (0,0) fits the pattern.

b)

It is a multiplicative pattern because Jerome’s points are multiplied by 6 to find Joaquin’s points.

c)

It is a multiplicative pattern because Jerome’s points are doubled to find Joaquin’s points.

d)

It is an additive pattern because 6 is added to Jerome’s points to find Joaquin’s points.

54.

What algebraic equation is represented by the graph?

a)

y = x + 4

b)

y = 4x

c)

y = x + 5

d)

y = 5x

55.

What type of relationship is represented by the table?

a)

Additive, because each y value is 4 more than the corresponding x value.

b)

Multiplicative, because each y value is 4 times the corresponding x value.

c)

Additive, because each y value is 5 more than the corresponding x value.

d)

Multiplicative, because each y value is 5 times the corresponding x value.

56.

Solve the Equation

m - 4 = 11

a)

13

b)

15

c)

18

d)

20

57.

Solve the Equation

q - 12 = 1

a)

11

b)

12

c)

13

d)

14

58.

Solve for x in the equation

x + 7 = 12

a)

3

b)

5

c)

9

d)

12

59.

Solve for z in the equation

3z = 15

a)

3

b)

4

c)

5

d)

6

60.

Solve for a in the equation

a + 5 = 10

a)

2

b)

5

c)

10

d)

15

61.

Solve for h in the equation

60h = 300

a)

4

b)

5

c)

6

d)

7

62.
What is the EQUATION for the problem below?

Ian spent $35 at the fair on ride tickets and admission.  It cost $5 to get into the fair and $2 per ride ticket.  How many ride tickets did Ian buy?
Let t = ride tickets
Equation:
a)
5t + 2 = 35
b)
7t = 35
c)
5 + t = 35
d)
5 + 2t = 35
63.
What is the EQUATION for the problem below?

Nick’s dog weighs 12 pounds more than Kiyah’s dog.  Kiyah's dog weighs 60 pounds.  How much does Nick’s dog weigh?
Let n = weight of Nick's dog
Equation:
a)
n + 12 = 60
b)
n - 12 = 60
c)
k + 12 = 60
d)
k - 12 = 60
64.
Last week Julia ran 30 miles more than Larry. Julia ran 47 miles in total. How many miles did Larry run?
a)
n + 47 = 30
b)
n + 30 = 47
c)
n - 30 = 47
d)
30n =47
65.

Jim paid a gym membership fee of $50, plus $20 per month. Jim has paid a total of $290 to the gym. Which equation matches this situation?

a)

50 + 20m = 290

b)

20 + 50m = 290

c)

50 + 20 = m

d)

50m - 20 = 290

66.

Scott works on cars. He charges $35 for each car plus $7 per hour. Write an equation that represents this scenario if Kylie's car bill was $63.

a)

7x + 35 = 63

b)

7x = 63

c)

7x - 35 = 63

d)

35x + 7 = 63

67.

Natalie is a softball coach. She has a private pitching lesson with Kasey. Kasey's mom pays Natalie $11 per hour plus a $6 tip. Write an equation that represents this scenario if the total cost was $39.

a)

11x + 6 = 39

b)

11x - 6 = 39

c)

11 + 6x = 39

d)

66x = 39

68.
WRITE AN EQUATION
For a field trip 4 students rode in cars and the rest filled nine buses. How many students were in each bus if 472 students were on the trip?
a)
4x=472
b)
9x=472
c)
4+9x=472
d)
4+x=472
69.
Hailey bought a book for $2.50 and 4 stickers.  She spent a total of 6.59.  How much did the stickers cost?
a)
$2.50 + 4s =$6.59
b)
$2.50s + 4 = $6.59
c)
$2.50 - 4s = $6.59
d)
4s - $2.50 = $6.59
70.
Cadin rents a bouncy house for a birthday party.  It costs $30.00 plus $4.00 per hour.  If he spends a total of $78.00, how many hours did he keep the bouncy house?
a)
$30.00 - $78.00 = $4.00h
b)
$78.00 + $30.00 = $4.00h
c)
$30.00 + $4.00h = $78.00
d)
$30.00 - $4.00h = $78.00
71.
Which choice models this situation?
Robyn had some video games, then bought 4 more.  Now she has a total of 10 games.
a)
v - 4 = 10
b)
v + 4 = 10
c)
10/4 = v
d)
4v = 10
72.

Which choice models this situation?


Lisa finished a race in 58 seconds. This was 4 seconds faster than her best practice time. What was Lindsey's best practice time?

a)

t + 4 = 58

b)

t - 4 = 58

c)

4t = 58

d)

t/4 = 58

73.

Which choice models this situation?


Jack needed new pencils for school today. He took 6 pencils from a new box of pencils. If there are 18 pencils left in the box, how many pencils were in the brand new box?

a)

p - 6 = 18

b)

p + 6 = 18

c)

6p = 18

d)

p/6 = 18

74.

Which choice models this situation?


Last week, James worked 35 hours in 5 days on the farm. He worked the same number of hours each day. How many hours did he work each day?

a)

h - 5 = 35

b)

h + 5 = 35

c)

5h = 35

d)

h/5 = 35

75.

Which of the following is part of the solution set?

a)

0, 1, 2

b)

-5, -4, -3

c)

3, 4, 5

d)

-2, 0, 2

76.

Which of the following is part of the solution set?

a)

0, 1, 2, 3

b)

5, 4, 3, 1

c)

2 ,3, 4, 5

d)

1, 2, 3, 5

77.

Which of the following is part of the solution set?

a)

-2, 0, 2, 4

b)

-5, -4, -3, -1

c)

-1, 0, 1, 3

d)

3, 0, -3, -5

78.

Which of the following is part of the solution set?

a)

-15, -10, -5, 0

b)

15, 10, 5, 0

c)

-3, 0, 3, 5

d)

-4, -2, 2, 4

79.

Which of the following has -1 in the solution set?

a)
b)
c)
d)
80.

Which of the following has -1 in the solution set?

a)
b)
81.

Which of the following has -10 in the solution set?

a)
b)
82.

Which of the following has 5 in the solution set? Select all that apply.

a)
b)
c)
d)
83.

x−5<12x-5<12  
Which of the following value for x makes the inequality true?

a)

17

b)

18

c)

16

d)

19

84.

w−4≥−8w-4\ge-8  
All of the following are a solution for the inequality except?

a)

-4

b)

-5

c)

0

d)

7

85.

Which number is in the solution set for the inequality?


2x > 45

a)

22.5

b)

20.5

c)

22

d)

43

86.

Which number is in the solution set for the inequality?

8−k≥508-k\ge50  

a)

48

b)

0

c)

-42

d)

42

87.

Tell whether the given value is a solution to the inequality
y + 4 < 16 ;  y = 13

a)

IS a solution

b)

IS NOT a solution

88.

Using the sign above, which of the following speeds are acceptable in front of the school?

a)

15

b)

8

c)

9

d)

10

e)

11

89.

51≥x+1051\ge x+10  
Which of the following values for x makes the inequality true?

a)

40

b)

41

c)

42

d)

43

e)

44

90.

w−4≥−8w-4\ge-8  
All of the following are a solution for the inequality except?

a)

-4

b)

-5

c)

0

d)

7

91.

m+11<−44m+11<-44  
Which of the following could be a solution for the inequality above?

a)

-50

b)

-60

c)

-55

d)

-40

92.

Tell whether the number is a solution to the inequality:

6 + w ≥ 12; when w = 5

a)

IS a solution

b)

Is NOT a solution

93.

Tell whether the number is a solution to the inequality:

11 + c ≥ 8; when c = -3

a)

IS a solution

b)

Is NOT a solution

94.

Tell whether the number is a solution to the inequality:

c - 4 ≤ 11; when c = -7

a)

IS a solution

b)

Is NOT a solution

95.

Tell whether the number is a solution to the inequality:

2 - x > -4; when x = 6

a)

IS a solution

b)

Is NOT a solution

96.
x + 7 > 15 if x = 10
a)
True
b)
False
97.
6m ≤ 30     if m = 5 
a)
True
b)
False
98.

Solve the equation: 3x + 5 = 17

a)

x = 7

b)

x = 4

c)

x = 10

d)

x = 2

99.

Solve the equation: 2x - 4 = 12

a)

x = 10

b)

x = 6

c)

x = 8

d)

x = 14

100.

Solve the inequality: 2x + 3 < 9

a)

x > 3

b)

x = 3

c)

x < 3

d)

x < 2

101.

Solve the inequality: 4x - 5 > 11

a)

x < 4

b)

x = 11

c)

x > 10

d)

x > 4

102.

Which number is a solution to the inequality: 3x + 2 > 11

a)

x = 3

b)

x > 3

c)

x < 3

d)

x = 2

103.
-4x + 14 ≤ 54
a)
x ≥ - 10
b)
x ≤ -10
c)
x ≥ 10
d)
x ≤ 10
104.

Solve the inequality 18<x4−218<\frac{x}{4}-2  

a)

80<x80<x  

b)

5<x5<x  

c)

4<x4<x  

d)

64<x64<x  

105.
a)

b)

c)

d)

106.

Match each statement with the correct graph.

a)
1.

y < 6

b)
2.

y > 6

c)
3.

y ≤ 6

d)
4.

y ≥ 6

107.

The solution to the inequality 5x − 4 > 21 is represented by which number line?

a)
b)
c)
d)
108.

What is the solution to the equation 342 = -18 - 18x?

a)

x = -20

b)

x = 20

c)

x = -40

d)

x = 40

109.
Solve:
-11x > 99
a)
x > -9
b)
x < -9
c)
x > 9
d)
x < 9
110.

Graph the inequality on a number line: 2y - 5 ≥ 7

a)

y > 6

b)

y ≤ 6

c)

y = 6

d)

y ≥ 6

111.

What is the value of y that satisfies the equation above?

a)

3

b)

9

c)

21

d)

63

112.

hint: need to get rid of the 3 first

a)

x ≥ 11

b)

x ≤ 19

c)

x < 11

d)

x > 19

113.
a)
x > 3
b)
x ≤ ⅕
c)
x ≥ 3
d)
x ≤ ⅕
114.

hint: move 11 first

a)

x ≤ 12

b)

x ≥ 12

c)

x ≥ 14

d)

x ≥ 23

115.
Does the given value make the inequality true?  x + 9 > 21, when x = 15
a)
True
b)
Not True

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