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Year 9 · Functions & Graphs

Gradient between two points

Gradient is how steep a line is: rise over run.

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How to do it

  1. Find the change in y (rise) between the points.
  2. Find the change in x (run).
  3. Divide rise by run. Simplify.

Worked example

What is the gradient of the line through A(0, 0) and B(-5, 2)?
Gradient = rise ÷ run = (y₂ − y₁) ÷ (x₂ − x₁) = (2 − 0) ÷ (-5 − 0) = 2 ÷ -5 = -2/5.
Answer: -2/5

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Going down from left to right gives a negative gradient.

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