Maths Library

Linear graphs and gradient: Year 8 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

Linear graphs and gradient is taught in Year 8 (age 13 to 14) as a topic to introduce. 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 Australian Curriculum v9. Check wording and codes against the official document.

  • AC9M8A05 Plot linear relationships and determine the gradient and equation of straight-line graphs.

Sample sheet and answers

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

Linear graphs and gradient

Year 8 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