AlgebraStructure & Method · Book 1All Chapters

Variation

8-9Direct Variation

Overview

y varies directly as x if y = kx (k ≠ 0). k is the constant of variation.

Key ideas

  • Doubling x doubles y.
  • Graph is a line through the origin.
  • Find k from one (x, y) pair.

Worked examples

Example 1

Problem. y varies directly with x. y = 12 when x = 3. Find y when x = 7.

Solution. k = 4. y = 4·7 = 28.

Practice

Try each one. Click Show answer when ready.

  1. 1.

    y = kx, y = 15 when x = 5. Find k.

  2. 2.

    y varies directly with x; y = 20 when x = 4. Find y when x = 10.

  3. 3.

    Does y = 2x represent direct variation?

Challenge problems

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

  1. 1.

    y varies directly with x. If y = 20 when x = 4, find y when x = 7.

  2. 2.

    The distance traveled varies directly with time. If 150 miles in 3 hours, how far in 5 hours?