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 y = kx that always passes through the origin — when one quantity doubles, so does the other.
Distance varies directly with time at constant speed: d = 60t.
Example 1
easy\(y\) varies directly with \(x\), and \(y = 18\) when \(x = 3\). Find the constant \(k\) and write the direct variation equation.
Example 2
mediumThe cost of fabric varies directly with length. 5 meters costs \$35. How much do 8 meters cost? Set up a proportion.
Example 3
easyIf \(y = kx\) and \(y = 24\) when \(x = 4\), find \(y\) when \(x = 7\).
Example 4
mediumA machine produces 150 units in 5 hours. Assuming direct variation, how many units in 9 hours?