8-10Inverse Variation

Overview

y varies inversely as x if y = k/x. As x increases, y decreases proportionally.

Key ideas

• xy = k (constant product).
• Graph is a hyperbola.
• Find k from one (x, y) pair.

Worked examples

Practice

Try each one. Click Show answer when ready.

1. 1.

   xy = 36. If x = 9, find y.

   Show answer
2. 2.

   y inversely varies with x; y = 10 when x = 2. Find y when x = 5.

   Show answer
3. 3.

   Does y = 5/x show inverse variation?

   Show answer

Challenge problems

A little tougher — great for test prep. Click Show answer when ready.

1. 1.

   y varies inversely with x. If y = 6 when x = 4, find y when x = 8.

   Show answer
2. 2.

   The time to complete a job varies inversely with the number of workers. If 4 workers take 6 hours, how long for 8 workers?

   Show answer