Chapter 10

Gradient of a Straight Line

Finding the gradient (steepness) of a line as rise over run — with an interactive exercise.

The gradient of a straight line measures its steepness.

Formula

Gradient $= \dfrac{\text{rise}}{\text{run}} = \dfrac{y_2 - y_1}{x_2 - x_1}$

Example: from $(1,1)$ to $(4,7)$, gradient $= \dfrac{7-1}{4-1} = \dfrac{6}{3} = 2$. A horizontal line has gradient 0.

Remember

  • Gradient = rise ÷ run.
  • Uphill (left→right) is positive; horizontal is 0.

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