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This topic recognises and uses graphs of direct and inverse proportion — straight lines through the origin for direct, reciprocal curves for inverse — and links them to their equations. It's a core topic in GCSE and iGCSE Maths with Edexcel and the other major boards. This free interactive eClassroom course walks through each step with worked examples and instant-feedback questions, so you can practise until it's secure.
How you do it
Direct proportion gives a straight line through the origin, and the gradient is the constant k. Inverse proportion gives a curve that approaches both axes without touching them. Reading k off the graph lets you write the equation.
Before you start
Get linear graphs and proportion straight before you begin. Getting it right here pays off in interpreting real-life graphs.
What you learn
When two quantities are in direct proportion their graph is a straight line through the origin. Such graphs let you convert between units and read off a rate — the gradient of the line tells you how much one quantity changes per unit of the other. A conversion graph is a straight line through the origin that converts one unit into another. For a proportion graph, the gradient (how steep the line is) gives the rate — the amount of change in y for each unit of x. Comparing two lines, the one with the greater gradient changes faster — for example, the better-value deal or the faster vehicle. The course works through conversion graphs, rate and gradient and interpreting proportion graphs. Every section has instant-feedback practice questions matched to Edexcel iGCSE 4MA1 and the other major GCSE boards, and the course finishes with full exam-style questions you mark yourself.
Related Topics
We teach Proportion Graphs as one of the Ratio and Proportion topics in our GCSE course library, at Foundation tier. The course is built from 3 concept sections, 2 worked examples and 3 check points before the exam-style set. Nearby topics in the same strand are Ratio, Ratio & Algebra and Similar Shapes. For unlimited practice, the Ratio and Proportion revision engine builds new questions on demand and records your accuracy.
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