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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 4

Curriculum topic:  Algebra

Curriculum subtopic:  Use y = mx + c to Identify Parallel and Perpendicular Lines

Difficulty level:  

down

Worksheet Overview

QUESTION 1 of 10

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

 

Remember that the line will have positive or negative gradient.

 

Example

Find the gradient of the straight line which passes through (8, 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 (8, 5) and (59).

 

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

 y-step = 5 - 9 = -4

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

x-step = 8 - 5 = 3

  

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

 

NB  We could have worked out 9 - 5 = 4 and 5 - 8 = -3 but 4 ÷ -3 = -4 ÷ 3

Find the gradient of the straight line which passes through:

(1, 5) and (5, 9)

 

(If it is not a whole number, write it as a fraction in the form a/b)

Find the gradient of the straight line which passes through:

(4, 12) and (5, 10)

 

(If it is not a whole number, write it as a fraction in the form a/b)

Find the gradient of the straight line which passes through:

(4, 2) and (5, 10)

 

(If it is not a whole number, write it as a fraction in the form a/b)

Find the gradient of the straight line which passes through:

(4, 2) and (5, -1)

 

(If it is not a whole number, write it as a fraction in the form a/b)

Find the gradient of the straight line which passes through:

(3, 8) and (5, 5)

 

(If it is not a whole number, write it as a fraction in the form a/b)

Find the gradient of the straight line which passes through:

(1, 2) and (4, 6)

 

(If it is not a whole number, write it as a fraction in the form a/b)

Find the gradient of the straight line which passes through:

(1, 14) and (4, 9)

 

(If it is not a whole number, write it as a fraction in the form a/b)

Find the gradient of the straight line which passes through:

(1, 4) and (5, 10)

 

(If it is not a whole number, write it as a reduced fraction in the form a/b)

Find the gradient of the straight line which passes through:

(6, 4) and (2, 0)

 

(If it is not a whole number, write it as a reduced fraction in the form a/b)

Find the gradient of the straight line which passes through:

(-6, 4) and (2, -2)

 

(If it is not a whole number, write it as a reduced fraction in the form a/b)

  • Question 1

Find the gradient of the straight line which passes through:

(1, 5) and (5, 9)

 

(If it is not a whole number, write it as a fraction in the form a/b)

CORRECT ANSWER
1
  • Question 2

Find the gradient of the straight line which passes through:

(4, 12) and (5, 10)

 

(If it is not a whole number, write it as a fraction in the form a/b)

CORRECT ANSWER
-2
  • Question 3

Find the gradient of the straight line which passes through:

(4, 2) and (5, 10)

 

(If it is not a whole number, write it as a fraction in the form a/b)

CORRECT ANSWER
8
  • Question 4

Find the gradient of the straight line which passes through:

(4, 2) and (5, -1)

 

(If it is not a whole number, write it as a fraction in the form a/b)

CORRECT ANSWER
-3
  • Question 5

Find the gradient of the straight line which passes through:

(3, 8) and (5, 5)

 

(If it is not a whole number, write it as a fraction in the form a/b)

CORRECT ANSWER
-3/2
  • Question 6

Find the gradient of the straight line which passes through:

(1, 2) and (4, 6)

 

(If it is not a whole number, write it as a fraction in the form a/b)

CORRECT ANSWER
4/3
  • Question 7

Find the gradient of the straight line which passes through:

(1, 14) and (4, 9)

 

(If it is not a whole number, write it as a fraction in the form a/b)

CORRECT ANSWER
-5/3
  • Question 8

Find the gradient of the straight line which passes through:

(1, 4) and (5, 10)

 

(If it is not a whole number, write it as a reduced fraction in the form a/b)

CORRECT ANSWER
3/2
  • Question 9

Find the gradient of the straight line which passes through:

(6, 4) and (2, 0)

 

(If it is not a whole number, write it as a reduced fraction in the form a/b)

CORRECT ANSWER
1
  • Question 10

Find the gradient of the straight line which passes through:

(-6, 4) and (2, -2)

 

(If it is not a whole number, write it as a reduced fraction in the form a/b)

CORRECT ANSWER
-3/4
---- OR ----

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