Fiducia TogetherDirect and inverse proportion graphs
What proportional relationships look like when plotted.
Please note: This page explains a word or a process in education. It is general information about the system, the law and the guidance in England — not advice about your child, your school or your exam. If a decision is going against you, get advice from one of the free services we link to before you agree to anything or miss a deadline. If you are revising, check your own exam board's specification: boards word things differently and yours is the one that marks you.
What it is
Direct proportion gives a straight line through the origin, y = kx. Inverse proportion gives a curve, y = k/x, approaching but never meeting the axes.
Where it applies
Both tiers; the algebraic forms are higher.
How it works
The shape identifies the relationship, and the constant k is found by substituting a known pair.
A straight line NOT through the origin is a linear relationship but not direct proportion, which is a distinction questions test.
How to use it in your work
Find k first, then answer the question. Two steps, both marked.
Check the line passes through the origin before calling it direct proportion.
Where to get help
Your teacher and your board's specification and mark scheme.
Revise this with a song
These are ours. We write revision songs because a lot of people remember a tune when they cannot remember a page, and because revising out loud in the kitchen beats staring at a highlighter.
- The Maths Song The GCSE maths topics, in order.
Where to read more
Last reviewed 2026-08-28 by Fiducia Together · Next review due 2027-08-28
Please note: This page explains a word or a process in education. It is general information about the system, the law and the guidance in England — not advice about your child, your school or your exam. If a decision is going against you, get advice from one of the free services we link to before you agree to anything or miss a deadline. If you are revising, check your own exam board's specification: boards word things differently and yours is the one that marks you.