Proportion Graphs and Equations [H]

This is a Higher-tier only topic that builds on the direct and inverse proportion work covered earlier. You need to recognise and interpret graphs of proportional relationships, set up equations involving squares, cubes, and square roots, and use them to solve problems. This topic connects algebra and proportion and is frequently tested on AQA Higher papers.

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Direct Proportion: y = kx

When y is directly proportional to x:

• The equation is y = kx
• The graph is a straight line through the origin
• The gradient of the line equals the constant k

Worked Example 1: y is directly proportional to x. When x = 5, y = 35. Find the equation and use it to find y when x = 12.

1. y = kx
2. 35 = k x 5, so k = 7
3. Equation: y = 7x
4. When x = 12: y = 7 x 12 = 84