Loading please wait

The smart way to improve grades

Comprehensive & curriculum aligned

Try an activity or get started for free

Gradient of a Line Given Two Points

In this worksheet, students calculate the gradient of a line which passes through two given points.

'Gradient of a Line Given Two Points' worksheet

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)

 

Answer 1

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

 

Answer 2

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?

 

What is EdPlace?

We're your National Curriculum aligned online education content provider helping each child succeed in English, maths and science from year 1 to GCSE. With an EdPlace account you’ll be able to track and measure progress, helping each child achieve their best. We build confidence and attainment by personalising each child’s learning at a level that suits them.

Get started
laptop

Try an activity or get started for free

  • educational
  • bettfutures
  • cxa
  • pta
  • era2016
  • BDA award
  • Explore LearningTuition Partner
  • tacm