Maths Library

Straight-line graphs and gradient: Year 9 maths

This topic explores linear functions, calculating gradients, and interpreting the equation y = mx + c. The worksheet provides practice in finding slopes, determining intercepts, and sketching or identifying lines.

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What this covers

Straight-line graphs and gradient is taught in Year 9 (age 13 to 14, KS3) as a main teaching focus. It sits in the Algebra strand.

Worked example

Find the gradient of the line passing through (1, 3) and (5, 11).

  1. Use the gradient formula: m = (y2 - y1) ÷ (x2 - x1)
  2. Substitute the coordinates: m = (11 - 3) ÷ (5 - 1)
  3. Simplify the fraction: m = 84 = 2

Answer: 2

Difficulty scale

The sheet generator offers five difficulty settings for this topic.

  1. Reading the gradient and y-intercept directly from y = mx + c
  2. Calculating positive integer gradients from two coordinates or a drawn line
  3. Calculating negative or fractional gradients and writing equations of lines
  4. Rearranging implicit equations into y = mx + c format, e.g., 2y - 4x = 8
  5. Finding equations of lines parallel or perpendicular to a given line

Common mistakes

  • Inverting the gradient formula to run over rise: (x2 - x1) / (y2 - y1)
  • Misidentifying the gradient when the equation is not written with y as the subject

Curriculum links

Indicative matches to National Curriculum for England. Check wording and codes against the official document.

  • Plot and interpret linear graphs, identifying the gradient and intercepts.

Sample sheet and answers

Six questions at the level's usual difficulty. Open the editor to change, add or regenerate any of them.

Straight-line graphs and gradient

Year 9 maths

Qs
6
Marks
6
NameDateScore / 6
1.
What is the gradient of y = −2x + 4?
[1]
2.
What is the gradient of y = −x + 3?
[1]
3.
What is the gradient of y = −3x − 1?
[1]
4.
What is the gradient of y = x − 2?
[1]
5.
What is the gradient of y = 2x + 3?
[1]
6.
What is the gradient of y = 3x + 1?
[1]

Answer key

  1. −2In y = mx + c the gradient is m, the number in front of x; Gradient = −2
  2. −1In y = mx + c the gradient is m, the number in front of x; Gradient = −1
  3. −3In y = mx + c the gradient is m, the number in front of x; Gradient = −3
  4. 1In y = mx + c the gradient is m, the number in front of x; Gradient = 1
  5. 2In y = mx + c the gradient is m, the number in front of x; Gradient = 2
  6. 3In y = mx + c the gradient is m, the number in front of x; Gradient = 3