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GCSE Maths / Edexcel

Straight-line graphs

Use y = mx + c to identify gradients, y-intercepts, and equations of straight lines.

AlgebraFoundation and HigherGrades 4 to 7Skill

Curriculum path: GCSE Maths > Edexcel > Algebra > Straight-line graphs

Pearson Edexcel GCSE Maths algebra A9 and A10: plot and interpret graphs, gradients, intercepts, and equations of straight lines.

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Revision notes

Theory, examples, and quick checks.

Keep the method short, then practise straight away. This note is written for GCSE Maths Edexcel students who need clear working and reliable method marks.

Theory

A straight-line graph can often be written as y = mx + c.

The gradient tells you the steepness and direction of the line. A positive gradient slopes up from left to right, and a negative gradient slopes down.

m is the gradient: how much y changes when x increases by 1.

c is the y-intercept: where the line crosses the y-axis. This happens when x = 0.

Gradient from two points is change in y divided by change in x. Many students lose marks by doing this the other way round.

For Edexcel graph questions, state both the calculation and the final equation if the question asks for an equation of a line.

Key ruleIn y = mx + c, m is the gradient and c is the y-intercept.

Worked examples

Read gradient and intercept

State the gradient and y-intercept of y = 2x + 3.

  1. Compare y = 2x + 3 with y = mx + c.
  2. m = 2 and c = 3.

Answer: Gradient 2, y-intercept 3

Build an equation

Find the equation of a line with gradient 4 and y-intercept -1.

  1. Use y = mx + c.
  2. m = 4 and c = -1.

Answer: y = 4x - 1

Use two points

Find the equation of the line through (0, 2) and (3, 8).

  1. Find the change in y: 8 - 2 = 6.
  2. Find the change in x: 3 - 0 = 3.
  3. Gradient = change in y / change in x = 6 / 3 = 2.
  4. The y-intercept is 2 because the line passes through (0, 2).

Answer: y = 2x + 2

Common mistakes

  • Mixing up the gradient and y-intercept.
  • Using change in x divided by change in y instead of change in y divided by change in x.
  • Forgetting that a negative gradient slopes down from left to right.
  • Reading the x-intercept instead of the y-intercept.

Quick exercise

Try these before moving to the exam-style questions.

  1. State the gradient of y = 5x + 2.
  2. State the y-intercept of y = -3x + 7.
  3. Find the equation with gradient 2 and y-intercept 6.
  4. Find the gradient between (1, 4) and (3, 10).
  5. Find the equation of the line through (0, -2) with gradient 4.
Exam-style questions

Practise the same skill at three levels.

These are original GCSE-style questions with mark schemes, common wrong answers, and AI marking guidance so feedback stays close to exam expectations.

Basic GCSE styleFoundationNon-calculator2 marks

For the line y = 3x + 2, state the gradient and the y-intercept.

straight-line graphsgradienty-intercept
Standard exam styleFoundation and HigherEither3 marks

Find the equation of the line with gradient -2 and y-intercept 5.

equation of a linenegative gradientmethod marks
ChallengeHigherEither4 marks

Find the equation of the line through (2, 7) and (5, 16).

gradient from two pointsline equationhigher algebra