The gradient of any line is how much it slopes.

We give a number to define how steep the line is.

A positive gradient means the line is up hill, a negative gradient means the line goes down hill.

To work out the exact gradient of a line, we take a section of it, and see how much its height changed between the start of the section and the end.

On a graph, we can do this really easily and accurately. Pick two points, and look at the difference between their x-coordinates and y-coordinates.

Then, just divide the difference in their y-coordinates, by the difference in their x-coordinates. That’s the gradient.

At either extreme, a gradient of 0 is perfectly horizontal/vertical, and an ‘undefined’ gradient (sometimes called a gradient of infinity) would be a perfectly vertical wall.

Example:

Suppose a linear graph has two coordinates at (2, 5) and (4, 10)

The difference in the x-coordinates is: 4-2 = 2 The difference in the y-coordinates is: 10-5 = 5

## Follow the links below to see how this topic has appeared in past exam papers

AQA Unit 2 November 2010 (H) - Page 11, Question 16

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