Practice Direct Variation in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

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Quick Recap

A proportional relationship y=kxy = kx that always passes through the origin — when one quantity doubles, so does the other.

Distance varies directly with time at constant speed: d=60td = 60t.

Showing a random 20 of 50 problems.

Example 1

easy
A line y=kxy = kx passes through (2,−8)(2, -8). Find kk.

Example 2

medium
A machine produces 150 units in 5 hours. Assuming direct variation, how many units in 9 hours?

Example 3

easy
Is y=3x+1y = 3x + 1 a direct variation?

Example 4

easy
If x=0x = 0 gives y=3y = 3, can the relation be a direct variation?

Example 5

medium
A spring obeys Hooke's law: stretch is directly proportional to force. A 4 N force stretches it 6 cm. How far does a 10 N force stretch it?

Example 6

easy
Distance varies directly with time: d=60td = 60t. Find dd at t=4t = 4.

Example 7

medium
The cost of fabric varies directly with length. 5 meters costs \$35. How much do 8 meters cost? Set up a proportion.

Example 8

medium
If yy varies directly with xx and y=9y = 9 when x=6x = 6, find xx when y=21y = 21.

Example 9

medium
Convert 60 miles per hour to a direct variation d=ktd = kt in miles for time tt in hours.

Example 10

medium
A graph of yy vs xx shows a straight line through (0,0)(0, 0) and (5,12)(5, 12). Write the direct variation.

Example 11

challenge
A relation has (x,y)=(3,12)(x,y) = (3,12) and (7,28)(7, 28). Decide if it is a direct variation and justify with kk.

Example 12

easy
If yy varies directly with xx and y=50y = 50 when x=10x = 10, find yy when x=25x = 25.

Example 13

easy
The constant of variation kk in y=8xy = 8x is ____.

Example 14

easy
An apple costs the same amount each. 4 apples cost $3. Write a direct variation for cost cc in terms of number of apples nn.

Example 15

easy
Write the direct variation where yy is always 44 times xx.

Example 16

hard
If yy varies directly with xx and the ordered pair (a,18)(a, 18) is on the graph y=2xy = 2x, find aa.

Example 17

challenge
Three jars of jam cost \$11.40. Use direct variation to find the cost of 17 jars.

Example 18

medium
Sarah's pay is a direct variation of hours worked: \$45 for 3 hours. How much does she earn in 11 hours?

Example 19

hard
yy varies directly with xx. Given y=12y = 12 when x=8x = 8, find the equation and use it to compute yy when x=50x = 50.

Example 20

easy
In a direct variation y=kxy = kx, when x=0x = 0, what is yy?
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