Fiducia TogetherGraphs and gradients
Straight lines, curves, and what the steepness means.
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
A straight line has the equation y = mx + c, where m is the gradient and c is where it crosses the y-axis. Gradient is the change in y divided by the change in x.
Where it applies
Both tiers. Higher adds quadratic, cubic, reciprocal and exponential graphs, and gradients of curves.
How it works
Gradient measures rate of change, which is why it means something in context: on a distance-time graph it is speed; on a velocity-time graph it is acceleration; on a cost graph, cost per unit.
Parallel lines share a gradient. Perpendicular gradients multiply to −1.
How to use it in your work
Always say what the gradient MEANS when a graph is in context. "The gradient is 4" scores less than "the gradient is 4, so the cost rises by £4 per item".
For curves, a tangent gives the gradient at a point — draw it long, and use it to read off a big triangle.
Where to get help
Your teacher, your board's specification for what is on your paper, and Bitesize for worked examples. The maths song runs the topics in order.
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.