GCSE & IGCSE maths practice

Straight line graphs (y = mx + c) questions and answers

A straight line has the equation $y = mx + c$ , where $m$ is the gradient (steepness) and $c$ is the y-intercept. The gradient between two points is $\dfrac{\text{change in } y}{\text{change in } x}$ . Parallel lines have the same gradient; perpendicular gradients multiply to $-1$ . Type equations as y = 2x + 3.

8 questions · Foundation and Higher tier · Every answer is checked as you type it, with a full worked solution. Updated 27 Oct 2026.

Start the questions Linear functions: lesson Equation of a line calculator

Where straight line graphs (y = mx + c) comes up

GCSE (AQA, Edexcel, OCR)	Foundation and Higher: gradients and intercepts, parallel lines, and the equation of a line through two points. Higher only: perpendicular lines.
Cambridge IGCSE (0580)	Core and Extended: gradient, the equation y = mx + c, and parallel lines. Extended only: perpendicular lines and perpendicular bisectors.

The method

Gradient m = (y₂ − y₁) ÷ (x₂ − x₁).
Find c by substituting a point into y = mx + c.
Rearrange other forms into y = mx + c to read off m and c.
Perpendicular gradient: −1 ÷ m (flip and change the sign).

Straight line graphs (y = mx + c) questions

Try each one before looking at the hint. If you're stuck, the AI tutor can talk you through it step by step.

Warm-up

Question 1Warm-upFoundation

Write down the gradient and y-intercept of $y = 3x - 2$ .

Gradienty-intercept

Question 2Warm-upFoundation

Find the gradient of the line through $(1, 2)$ and $(4, 11)$ .

Exam-style

Question 3Exam-styleFoundation

A line has gradient $-2$ and passes through $(0, 5)$ . Write down its equation.

y =

Question 4Exam-styleFoundation

Find the equation of the line through $(2, 7)$ and $(5, 13)$ .

y =

Question 5Exam-styleFoundation

What is the gradient of the line $4x + 2y = 10$ ?

Question 6Exam-styleFoundation

Find the equation of the line parallel to $y = 4x - 1$ that passes through $(1, -3)$ .

y =

Challenge

Question 7ChallengeHigher

What is the gradient of a line perpendicular to $y = 2x + 5$ ?

Question 8ChallengeHigher

Find the equation of the line perpendicular to $y = 2x + 1$ that passes through $(4, 3)$ .

y =

Common mistakes

Change in x over change in y (it's y over x).
Forgetting a negative gradient.
Reading the gradient of 2y = 6x + 4 as 6 (divide by 2 first).

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Sources

The questions are our own. The “where it comes up” notes are from each board's published specification, checked on 26 October 2026:

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