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Find the Gradient Between Two Points

In this worksheet, students will find the gradient between two points.

'Find the Gradient Between Two Points' worksheet

Key stage:  KS 4

Curriculum topic:  

Curriculum subtopic:  

Difficulty level:  

Worksheet Overview

QUESTION 1 of 10

The gradient of a line is its steepness.

You can find it by using the coordinates of two points.

If the first point has coordinates (xa, ya) and the second has coordinates (xb, yb), use the formula below to find the value of the gradient:

 

Let's have a look at an example.

Find the gradient of a line passing through (1, 3) and (4, 9).

The formula above means that we need to subtract y-coordinates of both points, subtract the x-coordinates and divide the former by the latter.

You can do this in stages or in one go using a calculator.

 

In stages:

9 - 3 = 6

4 - 1 = 3

6 ÷ 3 = 2

The gradient is 2.

 

Using a calculator:

This is what you need to put into your calculator:

The answer is 2.

Two points have coordinates (xa, ya) and (xb, yb).

What is the correct formula for finding the gradient of a line between these two points?





Find the gradient of a line passing through the points (3, 6) and (5, 8).

Find the gradient of a line between (5, 6) and (3, 10).

1/2

-1/2

2

-2

Find a gradient of a line between (10, -10) and (-2, -4).

-1/2

1/2

-2

2

Match the pairs of points with the gradients of lines between them.

Column A

Column B

(-9, 2) and (9, 12)
2/5
(5, 3) and (-2, -9)
5/9
(-3, 1) and (5, -12)
12/7
(-15, -3) and (0, 3)
-13/8

A line passes through two points: (-4, -1) and (-1, 4).

What is the gradient of this line?

5/3

3/5

-3/5

-5/3

True or False?

The gradient between (-3, -3) and (-4, 0) is -3.

True

False

True or False?

The gradient between (4, 8) and (3, 14) is 6.

True

False

Match the points below so that each pair has a line passing through it with a gradient of 3.

Column A

Column B

(1, 8)
(0, -3)
(-1, -1)
(2, 11)
(2, 2)
(4, 8)
(-3, -12)
(1, 5)

Find the gradient of a line between (-5, -1) and (-3, -7).

  • Question 1

Two points have coordinates (xa, ya) and (xb, yb).

What is the correct formula for finding the gradient of a line between these two points?

CORRECT ANSWER
EDDIE SAYS
The correct formula is this one:
  • Question 2

Find the gradient of a line passing through the points (3, 6) and (5, 8).

CORRECT ANSWER
1
EDDIE SAYS
The gradient here is 2. 8 - 6 = 2 5 - 3 = 2 2 ÷ 2 = 1
  • Question 3

Find the gradient of a line between (5, 6) and (3, 10).

CORRECT ANSWER
-2
EDDIE SAYS
Remember to subtract x and y coordinate values first and then divide the result of y-coordinates by this of x-coordinates. 10 - 6 = 4 3 - 5 = -2 (watch out for this minus here!) 4 ÷ -2 = -2
  • Question 4

Find a gradient of a line between (10, -10) and (-2, -4).

CORRECT ANSWER
-1/2
EDDIE SAYS
There is quite a few negative numbers here, so be careful, even if you are using a calculator! -4 - (-10) = -4 + 10 = 6 -2 - 10 = - 12 6 ÷ -12 = -6/12 = - 1/2
  • Question 5

Match the pairs of points with the gradients of lines between them.

CORRECT ANSWER

Column A

Column B

(-9, 2) and (9, 12)
5/9
(5, 3) and (-2, -9)
12/7
(-3, 1) and (5, -12)
-13/8
(-15, -3) and (0, 3)
2/5
EDDIE SAYS
All these answers are fractions which is quite common at GCSE level. If your answer is not an integer (whole number), then it's usually best to leave it as a fraction. Let's have a look at (-3, 1) and (5, -12). -12 - 1 = -13 5 - (-3) = 8 -13 ÷ 8 = -13/8
  • Question 6

A line passes through two points: (-4, -1) and (-1, 4).

What is the gradient of this line?

CORRECT ANSWER
5/3
EDDIE SAYS
How are you getting on with those negative numbers? The gradient is 5/3. Here's the method: 4 - (-1) = 5 -1 - (-4) = 3 5 ÷ 3 = 5/3 The gradient is 5/3.
  • Question 7

True or False?

The gradient between (-3, -3) and (-4, 0) is -3.

CORRECT ANSWER
True
EDDIE SAYS
This is true! 0 - (-3) = 3 -4 - (-3) = -1 (not 7!) 3 ÷ (-1) = -3.
  • Question 8

True or False?

The gradient between (4, 8) and (3, 14) is 6.

CORRECT ANSWER
False
EDDIE SAYS
Watch out! This statement is false. 14 - 8 = 6 3 - 4 = -1 6 ÷ -1 = -6 The gradient between (4, 8) and (3, 14) is - 6. Always check the signs carefully to make sure you have the correct answer.
  • Question 9

Match the points below so that each pair has a line passing through it with a gradient of 3.

CORRECT ANSWER

Column A

Column B

(1, 8)
(2, 11)
(-1, -1)
(1, 5)
(2, 2)
(4, 8)
(-3, -12)
(0, -3)
EDDIE SAYS
This is a slightly harder task as you need to check which coordinates go together to make a line with a gradient of 3. The best thing to do is to try some pairs and see if they give you an answer of 3 when you use the formula
  • Question 10

Find the gradient of a line between (-5, -1) and (-3, -7).

CORRECT ANSWER
-3
- 3
EDDIE SAYS
Watch out for these negative signs! It\'s always worth writing your calculations out as this helps you with checking for mistakes later. -7 - (-1) = -7 + 1 = -6 -3 - (-5) = -3 + 5 = 2 -6 ÷, 2 = -3
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