The gradient measures how steep a line is. Gradient = change in y ÷ change in x, often called rise over run. A line going up from left to right has a positive gradient; a line going down has a negative gradient.
For points A(−1, −6) and B(4, −3), the change in y is −3 − (−6) = 3 and the change in x is 4 − (−1) = 5, so the gradient is 3/5. A horizontal line has gradient 0. A steeper line has a bigger gradient.
Worked example
Find the gradient of the line through (1, 2) and (3, 10).
- Change in y: 10 − 2 = 8. Change in x: 3 − 1 = 2.
- 8 ÷ 2 = 4.
Answer:4
Key words
- gradient
- steepness: rise ÷ run
- rise
- the change in y
- run
- the change in x
Practise this
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Common Core-referenced: 8.EE.B.6, 8.F.B.4