Constant of proportionality worksheet

Grade 7 math, Common Core 7.RP.A.2b. 10 problems with an answer key and worked steps. Free to print, and you can make new problems any time.

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Constant of proportionality

Grade 7 math, Common Core 7.RP.A.2b

Find the constant of proportionality (k) in y = kx.

1.
A car goes 100 miles on 4 gallons of gas. What is the constant of proportionality in miles per gallon? Write an equation for miles m and gallons g.
2.
A car goes 198 miles on 9 gallons of gas. What is the constant of proportionality in miles per gallon? Write an equation for miles m and gallons g.
3.
The cost c of n pounds of grapes is proportional. 8 pounds cost $32.00. Write an equation.
4.
y = 1.2x. What is k?
5.
y = 0.75x. What is k?
6.
Find the constant of proportionality.
x 2 4 6 8
y 1 2 3 4
7.
The cost c of n pounds of grapes is proportional. 2 pounds cost $3.00. Write an equation.
8.
Find the constant of proportionality.
x 1 2 5 10
y 1.5 3 7.5 15
9.
y = 52x. What is k?
10.
A car goes 270 miles on 10 gallons of gas. What is the constant of proportionality in miles per gallon? Write an equation for miles m and gallons g.

x	2	4	6	8
y	1	2	3	4

x	1	2	5	10
y	1.5	3	7.5	15

Answer key: Constant of proportionality

Grade 7 math. Each answer has a few worked steps, to help check the method as well as the answer.

1. k = 25; m = 25g
100 ÷ 4 = 25
2. k = 22; m = 22g
198 ÷ 9 = 22
3. c = 4n
k = $32.00 ÷ 8 = 4
4. k = 1.2
5. k = 0.75
6. k = 0.5
1 ÷ 2 = 0.5
7. c = 1.5n
k = $3.00 ÷ 2 = 1.5
8. k = 1.5
1.5 ÷ 1 = 1.5
9. k = 52
10. k = 27; m = 27g
270 ÷ 10 = 27

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About constant of proportionality

In a proportional relationship y = kx, the number k is the constant of proportionality. It is the unit rate: how much y there is for each 1 of x. Find it by dividing y by x for any pair in a table or on a graph, or read it straight from the equation.

Worked example 1

A car goes 96 miles on 3 gallons of gas. What is the constant of proportionality in miles per gallon? Write an equation for miles m and gallons g.

Step 1.96 ÷ 3 = 32

Answer: k = 32; m = 32g

Worked example 2

The cost c of n pounds of grapes is proportional. 4 pounds cost $14.00. Write an equation.

Step 1.k = $14.00 ÷ 4 = 3.5

Answer: c = 3.5n

Example 3

y = 4.5x. What is k?

Answer: k = 4.5

Watch out for

k = y ÷ x, not x ÷ y.
k can be a fraction or a decimal, like 34 or 2.5.
In a word problem, k has units, like miles per gallon.

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