Gradient

Definition

The gradient of a straight line measures its steepness and direction. It is the change in y divided by the change in x between any two points on the line. In y = mx + c, the gradient is m.

Worked example

The line through (1; 2) and (3; 8) has gradient m = (8 − 2) ÷ (3 − 1) = 3.

y = −3x + 5 has gradient −3: it slopes downwards from left to right.

A horizontal line such as y = 4 has gradient 0.

Where it appears in the exam

Gradient is part of the graphs section of CAPS Grade 9 Mathematics and appears in school tests and the end-of-year exam.

Step-by-step method

1. Choose two points on the line, (x₁; y₁) and (x₂; y₂).
2. Subtract the y-values: y₂ − y₁.
3. Subtract the x-values in the same order: x₂ − x₁.
4. Divide: m = (y₂ − y₁) ÷ (x₂ − x₁).

Common mistake

Dividing the change in x by the change in y, which gives the reciprocal of the gradient.

Related graphs terms

• y-intercept

Frequently asked questions

What does gradient mean in Grade 9 Maths?

The gradient of a straight line measures its steepness and direction. It is the change in y divided by the change in x between any two points on the line. In y = mx + c, the gradient is m.

When do you learn about gradient?

Gradient is taught in the graphs section of CAPS Grade 9 Mathematics and is used again in Grades 10 to 12.

How do I practise questions involving gradient?

Snap a question that uses gradient into Snap&Learn with your grade set to Grade 9, or work through the Grade 9 topic guide and practice papers.