Equation of a straight line: y = mx + c
The equation of a straight line is y = mx + c, or y − y₁ = m(x − x₁) through the point (x₁, y₁).
What each letter means
- \(m\) the gradient (slope)
- \(c\) the y-intercept: where the line crosses the y-axis
- \((x_1,\ y_1)\) a point on the line
When to use it
To write the equation of a line from its gradient and one point, or from two points (find the gradient first). Use y − y₁ = m(x − x₁) when the point is not on the y-axis.
Worked example
Find the equation of the line through \((-3,4)\) and \((1,-4)\) in the form \(y=mx+c\).
- \(m=\dfrac{-4-4}{1-(-3)}=\dfrac{-8}{4}=-2\)
- \(y-4=-2(x+3)\), so \(y=-2x-6+4\)
Answer: \(y=-2x-2\)
Common mistake
Sign slips with a negative coordinate: through (−3, 4) the equation is y − 4 = m(x + 3), not m(x − 3).
On your course
| Course | In the exam |
|---|---|
| Edexcel A Level (9MA0) | Not in the Edexcel booklet: learn it |
| Edexcel International A Level | Not in the booklet: learn it |
| AQA or OCR A Level | Check your board’s formula booklet: AQA formulae booklet (PDF) · OCR A Level Maths assessment page |
From our own A Level Maths formula sheets, in our words. Official: Pearson's formulae booklet (PDF) · Pearson's IAL formulae booklet (PDF).
Practise and revise
- Practise A Level Maths practice
- Revise Coordinate geometry
- Revise IAL P1 coordinate geometry
- Print Edexcel A Level (9MA0) one-page formula sheet
Questions
What is the equation of a straight line formula?
The equation of a straight line is y = mx + c, or y − y₁ = m(x − x₁) through the point (x₁, y₁). m: the gradient (slope); c: the y-intercept: where the line crosses the y-axis; (x₁, y₁): a point on the line.
Is the equation of a straight line given in the exam?
Edexcel A Level (9MA0): not in the Edexcel booklet: learn it. Edexcel International A Level: not in the booklet: learn it. AQA or OCR A Level: check your board’s formula booklet. This comes from our own A Level Maths formula sheets; your teacher has the official booklet.
How do I find the equation of a line through two points?
Find the gradient m = (y₂ − y₁) ÷ (x₂ − x₁), then put m and either point into y − y₁ = m(x − x₁) and rearrange.
Our own wording, examples and card, checked by A Level Math Revision. Not produced or endorsed by Pearson Edexcel, AQA or OCR.