Proportion equations

Proportion equations describe how one quantity depends on another. In direct proportion y = kx: double x and y doubles. In inverse proportion y = k/x: double x and y halves. Other forms include y = kx² and y = k/√x.

Key facts

  • Direct: y = kx. Inverse: y = k/x.
  • Find k by putting in one known pair of values.
  • y ∝ x²: doubling x multiplies y by 4.
  • Graphs: direct is a straight line through the origin; inverse is a curve that never touches the axes.

Worked examples

Example 1

y is inversely proportional to x. y = 12 when x = 3. Find y when x = 9.

  1. y = k/x so 12 = k/3. k = 36
  2. y = 36/9 = 4

Answer: 4

Example 2

The stopping distance d is proportional to the square of the speed v. d = 18 m when v = 30 km/h. Find d when v = 60 km/h.

  1. d = kv²: 18 = k × 900, k = 0.02.
  2. d = 0.02 × 3600 = 72

Answer: 72 m