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AQASpec A9-A11Foundation & Higher~30 min

Straight Line Graphs

Mathematics · Topic revision workspace

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Topic overview

What you need to know

Straight Line Graphs is a key part of GCSE Mathematics. Build fluency with the method, then apply it to unfamiliar and multi-step problems. A measure of how steep a line is. Calculated as rise ÷ run, or (y₂ − y₁) ÷ (x₂ − x₁). The equation of a straight line where m is the gradient and c is the y-intercept. The point where a line crosses the y-axis. In y = mx + c, the y-intercept is (0, c).

Exam tip

Write every stage of your method. Method marks can still be earned when the final answer is wrong.

Revision notes

Core ideas

Secure these ideas first. Say each definition in your own words, then connect it to the topic overview.

  • Gradient (Slope): A measure of how steep a line is. Calculated as rise ÷ run, or (y₂ − y₁) ÷ (x₂ − x₁).
  • y = mx + c: The equation of a straight line where m is the gradient and c is the y-intercept.
  • y-intercept: The point where a line crosses the y-axis. In y = mx + c, the y-intercept is (0, c).
  • Parallel Lines: Lines with the same gradient but different y-intercepts. They never intersect.

Revision notes

Apply it in the exam

The exam will rarely ask for an isolated definition. Practise selecting the right idea and using it as part of a complete explanation or method.

  • Perpendicular Lines: Lines whose gradients multiply to give −1. If one gradient is m, the other is −1/m.
  • x-intercept: The point where a line crosses the x-axis. Found by setting y = 0 and solving for x.
  • Positive Gradient: A line that slopes upward from left to right has a positive gradient.
  • Finding the Equation of a Line: Use y − y₁ = m(x − x₁) with the gradient m and a known point (x₁, y₁).

Core knowledge

Key facts for Straight Line Graphs

1

Gradient (Slope)

A measure of how steep a line is. Calculated as rise ÷ run, or (y₂ − y₁) ÷ (x₂ − x₁).

2

y = mx + c

The equation of a straight line where m is the gradient and c is the y-intercept.

3

y-intercept

The point where a line crosses the y-axis. In y = mx + c, the y-intercept is (0, c).

4

Parallel Lines

Lines with the same gradient but different y-intercepts. They never intersect.

5

Perpendicular Lines

Lines whose gradients multiply to give −1. If one gradient is m, the other is −1/m.

6

x-intercept

The point where a line crosses the x-axis. Found by setting y = 0 and solving for x.

7

Positive Gradient

A line that slopes upward from left to right has a positive gradient.

8

Finding the Equation of a Line

Use y − y₁ = m(x − x₁) with the gradient m and a known point (x₁, y₁).

Active recall

Close the notes and answer these

  1. 1.Without looking, explain gradient (slope) and give one example or consequence.
  2. 2.Without looking, explain y = mx + c and give one example or consequence.
  3. 3.Without looking, explain y-intercept and give one example or consequence.
  4. 4.Without looking, explain parallel lines and give one example or consequence.

Content reviewed 23 July 2026 against the current linked specification.

Finished learning?

Mark the notes complete, then test what you can recall.

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