# 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:

### 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

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

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:

(1, 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, 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, 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:

(3, 2) 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, 4) 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:

(10, 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)

1
EDDIE SAYS
 Gradient of line  = 9 - 5 = 4 = 1 5 - 1 4
• Question 2

Find the gradient of the straight line which passes through:

(1, 2) and (5, 10)

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

2
EDDIE SAYS
 Gradient of line  = 10 - 2 = 8 = 2 5 - 1 4
• 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)

8
EDDIE SAYS
 Gradient of line  = 10 - 2 = 8 = 8 5 - 4 1
• Question 4

Find the gradient of the straight line which passes through:

(4, 2) and (5, 5)

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

3
EDDIE SAYS
 Gradient of line  = 5 - 2 = 3 = 3 5 - 4 1
• Question 5

Find the gradient of the straight line which passes through:

(3, 2) and (5, 5)

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

3/2
EDDIE SAYS
 Gradient of line  = 5 - 2 = 3 = 3/2 5 - 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)

4/3
EDDIE SAYS
 Gradient of line  = 6 - 2 = 4 = 4/3 4 - 1 3
• Question 7

Find the gradient of the straight line which passes through:

(1, 4) and (4, 9)

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

5/3
EDDIE SAYS
 Gradient of line  = 9 - 4 = 5 = 5/3 4 - 1 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)

3/2
EDDIE SAYS
 Gradient of line  = 10 - 4 = 6 = 3/2 5 - 1 4
• 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)

1
EDDIE SAYS
 Gradient of line  = 0 - 4 = -4 = 1 2 - 6 -4
• Question 10

Find the gradient of the straight line which passes through:

(10, 4) and (2, -2)

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

3/4
EDDIE SAYS
 Gradient of line  = -2 - 4 = -6 = 3/4 2 - 10 -8
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