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AQA GCSE Maths

Graphs: straight lines, curves and interpreting rates — AQA GCSE Maths revision

Free revision notes, key terms, common exam traps and 5 practice questions with answers. About 7 minutes to read.

Straight-line graphs

  • y = mx + c: m is the gradient, c is the y-intercept.
  • Gradient between two points = (y2 − y1) ÷ (x2 − x1).
  • Parallel lines have equal gradients; perpendicular lines have gradients that multiply to −1.

Curves and quadratics

  • y = x^2 gives a parabola shape; the graph of y = -x^2 is reflected upside down.
  • Roots of a quadratic are where the graph crosses the x-axis (y = 0).
  • The turning point of a parabola is its minimum (positive x^2) or maximum (negative x^2).

Key terms

Gradient
The steepness of a line, calculated as change in y ÷ change in x.
y-intercept
The point where a graph crosses the y-axis, given by c in y = mx + c.
Parabola
The curved shape of a quadratic graph.
Turning point
The maximum or minimum point on a curve.
Root
A value of x where the graph crosses the x-axis (y = 0).
Rate of change
How quickly one variable changes with respect to another, shown by gradient.

Common exam traps

  • Confusing gradient (m) with y-intercept (c) in y = mx + c.
  • Forgetting the negative reciprocal rule for perpendicular gradients.
  • Reading a flat section of a distance-time graph as movement instead of rest.

Practice questions with answers

  1. 1. Find the gradient of the line y = 3x + 5.

    Answer: 3

    In y = mx + c, m is the gradient, so m = 3.

  2. 2. Find the y-intercept of y = -2x + 7.

    Answer: 7

    c = 7, so the graph crosses the y-axis at (0,7).

  3. 3. Find the gradient of the line through (1,2) and (3,8).

    Answer: 3

    (8-2)/(3-1) = 6/2 = 3.

  4. 4. A line has gradient 2. Find the gradient of a line perpendicular to it.

    • • 2
    • • -2
    • • 1/2
    • • -1/2

    Answer: -1/2

    Perpendicular gradients multiply to -1: 2 × (-1/2) = -1.

  5. 5. Find the equation of a line parallel to y = 4x - 1 passing through (0, 3).

    Answer: y = 4x + 3

    Parallel lines share gradient 4; y-intercept becomes 3.

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