Maths Library

Straight-line graphs and gradient: Year 11 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 11 (age 15 to 16, KS4) 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.

  • Determine the equation of a straight line, identifying parallel and perpendicular gradients.

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 11 maths

Qs
6
Marks
12
NameDateScore / 12
1.
Write the equation of the line in the form y = mx + c.
-5-5-4-4-3-3-2-2-1-11122334455
[2]
2.
Write the equation of the line in the form y = mx + c.
-5-5-4-4-3-3-2-2-1-11122334455
[2]
3.
Write the equation of the line in the form y = mx + c.
-5-5-4-4-3-3-2-2-1-11122334455
[2]
4.
Write the equation of the line in the form y = mx + c.
-5-5-4-4-3-3-2-2-1-11122334455
[2]
5.
Write the equation of the line in the form y = mx + c.
-5-5-4-4-3-3-2-2-1-11122334455
[2]
6.
Write the equation of the line in the form y = mx + c.
-5-5-4-4-3-3-2-2-1-11122334455
[2]

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