Practice Direct Variation in Math
Use these practice problems to test your method after reviewing the concept explanation and worked examples.
Quick Recap
A proportional relationship that always passes through the origin — when one quantity doubles, so does the other.
Distance varies directly with time at constant speed: .
Showing a random 20 of 50 problems.
Example 1
easyA line passes through . Find .
Example 2
mediumA machine produces 150 units in 5 hours. Assuming direct variation, how many units in 9 hours?
Example 3
easyIs a direct variation?
Example 4
easyIf gives , can the relation be a direct variation?
Example 5
mediumA 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
easyDistance varies directly with time: . Find at .
Example 7
mediumThe cost of fabric varies directly with length. 5 meters costs $35. How much do 8 meters cost? Set up a proportion.
Example 8
mediumIf varies directly with and when , find when .
Example 9
mediumConvert 60 miles per hour to a direct variation in miles for time in hours.
Example 10
mediumA graph of vs shows a straight line through and . Write the direct variation.
Example 11
challengeA relation has and . Decide if it is a direct variation and justify with .
Example 12
easyIf varies directly with and when , find when .
Example 13
easyThe constant of variation in is ____.
Example 14
easyAn apple costs the same amount each. 4 apples cost $3. Write a direct variation for cost in terms of number of apples .
Example 15
easyWrite the direct variation where is always times .
Example 16
hardIf varies directly with and the ordered pair is on the graph , find .
Example 17
challengeThree jars of jam cost $11.40. Use direct variation to find the cost of 17 jars.
Example 18
mediumSarah's pay is a direct variation of hours worked: $45 for 3 hours. How much does she earn in 11 hours?
Example 19
hard varies directly with . Given when , find the equation and use it to compute when .
Example 20
easyIn a direct variation , when , what is ?