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 of the form y = kx (where k \neq 0) that always passes through the origin; when one quantity doubles, the other doubles, and the ratio \frac{y}{x} remains constant.

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

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

Example 3

easy
If \(y = kx\) and \(y = 24\) when \(x = 4\), find \(y\) when \(x = 7\).

Example 4

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