Gradient formula: m = (y₂ − y₁) / (x₂ − x₁)
The gradient formula is gradient m = (y₂ − y₁) / (x₂ − x₁).
What each letter means
- \(m\) the gradient (slope) of the line
- \((x_1,\ y_1),\ (x_2,\ y_2)\) two points on the line
When to use it
To find how steep a line is from two points on it, before writing its equation y − y₁ = m(x − x₁).
Worked example
Find the gradient of the line through \((1,-3)\) and \((4,9)\).
- \(m=\dfrac{9-(-3)}{4-1}=\dfrac{12}{3}\)
Answer: \(m=4\)
Common mistake
Putting the x difference on top. Gradient is rise over run: change in y ÷ change in x.
On your course
| Course | In the exam |
|---|---|
| Edexcel 4MA1 (Higher) | Not given: learn it |
| Cambridge 0580 | Not given: learn it (Extended only) |
From our own IGCSE Maths formula sheets, in our words. Official: Pearson's 4MA1 specification (PDF, Appendix 5) · Cambridge's 0580 syllabus (PDF).
Practise and revise
Questions
What is the gradient formula?
The gradient formula is gradient m = (y₂ − y₁) / (x₂ − x₁). m: the gradient (slope) of the line; (x₁, y₁), (x₂, y₂): two points on the line.
Is the gradient formula given in the exam?
Edexcel 4MA1 (Higher): not given: learn it. Cambridge 0580: not given: learn it (Extended only). This comes from our own IGCSE Maths formula sheets; your teacher has the official booklet.
What are the gradients of parallel and perpendicular lines?
Parallel lines have equal gradients. Perpendicular gradients multiply to −1, so a line perpendicular to gradient m has gradient −1/m.
Our own wording, examples and card, checked by IGCSE Math Revision. Not produced or endorsed by Pearson Edexcel.