Loading please wait

The smart way to improve grades

Comprehensive & curriculum aligned

Try an activity or get started for free

Find the Gradient of a Line Given Two Points

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

'Find the Gradient of a Line Given Two Points' worksheet

Key stage:  KS 3

Year:  Year 9 Maths worksheets

Curriculum topic:   Algebra

Curriculum subtopic:   Solve Linear Equations (One Variable)

Popular topics:   Algebra worksheets

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.

 

The rule to remember is:

 

The gradient of a line = y-step ÷ x-step

 

Example

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

 

Answer 1

Let's look at the line drawn on a set of x-y coordinate axes.

 

gradient line on coordinate grid

 

The vertical part of the step (y-step) = 4

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

 

The gradient of the line = y=step ÷ x-step = 4 ÷ 3 = 4/3 

 

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

 

The gradient of the line = y-step ÷ x-step = 4 ÷ 3 = 4/3 

  

 

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

Popular Maths topics

Try an activity or get started for free

  • National Tutoring Awards 2023 Shortlisted / Parents
    National Tutoring Awards 2023 Shortlisted
  • Private-Tutoring-WINNER-EducationInvestor-Awards / Parents
    Winner - Private Tutoring
  • Bett Awards Finalist / Parents
    Finalist
  • Winner - Best for Home Learning / Parents
    Winner - Best for Home Learning / Parents