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Constant of Proportionality - Printable Mathematics Worksheets class 7 - Wayground

Constant of Proportionality

15 questions

7th - 7th Grade

Mathematics

This Grade 7 mathematics worksheet develops students’ understanding of the constant of proportionality in tables, equations, and graphs. Students determine whether relationships are proportional, calculate the constant k, write equations in the form y = kx, identify direct variation, and interpret ordered pairs and axes on proportional graphs. The worksheet includes 15 questions: 14 multiple-choice items and one multiple-select question about graph statements. Use this resource to reinforce how the same proportional relationship can be represented numerically, algebraically, and visually. Students compare proportional and non-proportional relationships, work with whole numbers, fractions, decimals, rates, and a negative constant, and select all graph interpretations supported by the data. This free printable worksheet includes a complete answer key for independent practice, homework, intervention, or a Grade 7 mathematics check for understanding.

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Constant of Proportionality

Total questions: 15

Name
Class
Date
1.
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
2.
Write the equation for the table given.
a)
y = 16x
b)
y=8x
c)
y=12x
3.
What is the constant of proportionality for this table?
a)
$1/9 per hour
b)
$9 per hour
c)
$8 per hour
4.

Is this table proportional or non-proportional?

a)

Yes

b)

No

5.
Write an equation for this relationship.
a)
y = 18x
b)
y = 18.50x
c)
y = 22.50x
d)
y = 22x
6.
What is the direct variation?
a)
y=9/3x
b)
y=6x
c)
y=9x
d)
y=3x
7.

Identify the constant of proportionality.

a)

k = 2x

b)

k = 2

c)

k = 4

d)

none (not proportional)

8.

Identify the constant of proportionality.

a)

k = 2

b)

k = 3

c)

k = 1.50

d)

k = 2/3

e)

none (not proportional)

9.

Identify the constant of proportionality.

a)

k = 2

b)

k = 4

c)

k = 1/2

d)

k = 1/4

e)

none (not proportional)

10.

Identify the constant of proportionality.

a)

k = 1/0.45

b)

k = 0.45

c)

k = -0.45

d)

k = -1/0.45

e)

none (not proportional)

11.

Which of the following statements is TRUE about the graph? Choose all that apply.

a)

The point (2, 8) shows that 8 pounds of cheese cost$2.00.

b)

The point (1.5, 6) shows the cost is $6.00 for 1.5pounds of cheese.

c)

The point (0.75, 3) shows that 0.75 pound of cheesecosts $3.00.

d)

The point (0.25, 1) shows the cost is $0.25 for 1pound of cheese.

e)

The point (0, 0) shows the cost is $0.00 for 0 pounds of cheese

12.
The horizontal axis is the y-axis.
a)
True
b)
False
13.
Which of the tables above represents a proportional relationship?
a)
a & c
b)
a, b & c
c)
a, c & d
d)
all of them
14.
Which best describes the graph represented in this table?
a)
 proportional
b)
non-proportional
15.
Which graph is proportional?
a)
A
b)
B
c)
C and D
d)
All of the graphs are proportional
Answer Key

Constant of Proportionality

Total questions: 15

1.
b) Yes; 3
2.
b) y=8x
3.
b) $9 per hour
4.
a)

Yes

5.
b) y = 18.50x
6.
d) y=3x
7.
b)

k = 2

8.
c)

k = 1.50

9.
e)

none (not proportional)

10.
c)

k = -0.45

11.
b)

The point (1.5, 6) shows the cost is $6.00 for 1.5pounds of cheese.

, c)

The point (0.75, 3) shows that 0.75 pound of cheesecosts $3.00.

, e)

The point (0, 0) shows the cost is $0.00 for 0 pounds of cheese

12.
b) False
13.
c) a, c & d
14.
a)  proportional
15.
d) All of the graphs are proportional

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FAQs

What does this constant of proportionality worksheet cover?

This Grade 7 worksheet asks students to identify proportional and non-proportional relationships, calculate the constant of proportionality k, write equations such as y = kx, and interpret proportional tables and graphs. Its 14 multiple-choice questions and one multiple-select question require students to connect constants, equations, ordered pairs, rates, axis labels, and graph representations.

How can I use this worksheet to teach students about the constant of proportionality?

Introduce the worksheet by modeling how to divide a y-value by its corresponding x-value to find k, then use y = kx to verify the relationship and write its equation. Have students explain why some tables or graphs are proportional and discuss how points such as (1.5, 6) represent two related quantities. Finish by asking students to justify each selected statement in the multiple-select graph question using the coordinates and axis meanings.

What mistakes should I watch for when students complete this worksheet?

Students may reverse the quantities when calculating k, choose a reciprocal such as 1/0.45 instead of the correct rate, or write the wrong coefficient in y = kx. Watch for confusion between proportional and non-proportional tables, misreading the horizontal axis as the y-axis, and reversing the meaning of coordinates in the cheese-cost graph. In the multiple-select item, students may select statements that swap the x- and y-values or overlook that (0, 0) represents zero cost for zero pounds.

How do I assign and grade this constant of proportionality worksheet?

The worksheet is available as a printable PDF and as a digital quiz on Wayground, so you can assign the 15 items in the format that fits your lesson. It includes a complete answer key, and printable submissions can be graded by scanning student work with the Wayground for Teachers app. The printable option can also support classrooms that are reducing screen time.

How can I differentiate this worksheet for my students?

Use the worksheet’s Advanced Settings to adjust font spacing or increase the font size so the tables, equations, and graph-based prompts are easier to read. You can also apply a dyslexia-friendly font or translate the worksheet into another language while keeping the constant-of-proportionality practice and question format intact.

Where can I find more worksheets like this on Wayground?

Wayground offers a broad collection of free printable worksheets and practice problems across subjects, with downloadable PDFs and answer keys to support essential skills and concepts. Browse more resources at https://wayground.com/en-us/worksheets.

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