  # Gradient of a Line Given Two Points

In this worksheet, students calculate the gradient of a line which passes through two given points. Key stage:  KS 3

Curriculum topic:   Algebra

Curriculum subtopic:   Solve Linear Equations (One Variable)

Difficulty level:   #### Worksheet Overview

It is possible to work out the gradient of a straight line from the coordinates of any two points which lie on the line, either by drawing the line or simply by subtracting and dividing coordinates.

 Gradient of line  = y-step x-step

Example

Find the gradient of the straight line which passes through (2, 5) and (5, 9)

Let's look at the line drawn on a set of x-y coordinate axes. The vertical part of the step (y-step) = 4

The horizontal part of the step (x-step) = 3

 Gradient of line  = y-step = 4 x-step 3

It is possible to work out the gradient WITHOUT drawing the line.

Look at the coordinates of the two points (2, 5) and (59).

We can get the y-step by subtracting the y-coordinates.

y-step = 9- 5 = 4

In the same order, we get the x-step by subtracting the x-coordinates:

x-step = 5 - 2 = 3

 Gradient of line  = y-step = 4 x-step 3

NB: We could have worked out 5 - 9 = -4 and 2 - 5 = -3 but -4 ÷ -3 = 4 ÷ 3

Want a bit more help with this before you begin? Why not watch this short video?

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