Maths Library

Straight-line graphs and gradient: Year 13 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 13 (age 17 to 18, KS5) 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 National Curriculum for England. Check wording and codes against the official document.

  • Apply properties of gradients and tangents to solve geometric problems involving straight lines and curves.
  • Determine intersections and parallel or perpendicular lines within coordinate geometry and vector frameworks.

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 13 maths

Qs
6
Marks
24
NameDateScore / 24
1.
Write the equation of the line in the form y = mx + c.
-5-5-4-4-3-3-2-2-1-11122334455
[4]
2.
Write the equation of the line in the form y = mx + c.
-5-5-4-4-3-3-2-2-1-11122334455
[4]
3.
Write the equation of the line in the form y = mx + c.
-5-5-4-4-3-3-2-2-1-11122334455
[4]
4.
Write the equation of the line in the form y = mx + c.
-5-5-4-4-3-3-2-2-1-11122334455
[4]
5.
Write the equation of the line in the form y = mx + c.
-5-5-4-4-3-3-2-2-1-11122334455
[4]
6.
Write the equation of the line in the form y = mx + c.
-5-5-4-4-3-3-2-2-1-11122334455
[4]

Answer key

  1. y = −2x + 4The line crosses the y-axis at 4, so c = 4; It goes −2 up for each 1 across, so m = −2
  2. y = −x + 3The line crosses the y-axis at 3, so c = 3; It goes −1 up for each 1 across, so m = −1
  3. y = −3x − 1The line crosses the y-axis at −1, so c = −1; It goes −3 up for each 1 across, so m = −3
  4. y = x − 2The line crosses the y-axis at −2, so c = −2; It goes 1 up for each 1 across, so m = 1
  5. y = 2x + 3The line crosses the y-axis at 3, so c = 3; It goes 2 up for each 1 across, so m = 2
  6. y = 3x + 1The line crosses the y-axis at 1, so c = 1; It goes 3 up for each 1 across, so m = 3