Topics
11. Coordinate Geometry
topic badge
iGCSE (2021 Edition)

11.12 Finding the equation from a graph

Lesson
Worksheet
Practice
Worksheet
Equations of lines
1

Determine whether the following graphs are linear:

a
-4
-3
-2
-1
1
2
3
4
x
-4
-3
-2
-1
1
2
3
4
y
b
-4
-3
-2
-1
1
2
3
4
x
-2
-1
1
2
3
4
5
6
7
8
9
y
c
-4
-3
-2
-1
1
2
3
4
x
-1
1
2
3
4
5
y
d
-2
-1
1
2
3
4
5
6
x
-4
-3
-2
-1
1
2
3
4
y
2

Consider the following graph:

a

Complete the table of values for the points shown on the line.

x-1012
y
b

State the values of the gradient m, and the y-intercept, c.

c

Given that the linear relationship is in the form y = m x + c, write the equation of the line.

d

Hence find the coordinates for the point on the line when x = 21.

-5
-4
-3
-2
-1
1
2
3
4
5
x
-6
-5
-4
-3
-2
-1
1
2
3
4
5
6
y
3

Consider the following graph:

a

Complete the table of values for the points shown on the line.

x-1012
y
b

State the values of the gradient m, and the y-intercept, c.

c

Hence write the linear equation for the line in gradient-intercept form.

d

Find the coordinates for the point on the line where x = 27.

-4
-3
-2
-1
1
2
3
4
x
-3
-2
-1
1
2
3
4
5
6
7
8
y
4

Consider the following graph:

a

Complete the table of values for the points shown on the line:

x-2-101
y
b

State the values of the gradient m, and the y-intercept, c.

c

Hence write the equation for the line in gradient-intercept form.

d

Find the value of y when x = 40.

-4
-3
-2
-1
1
2
3
4
x
-8
-7
-6
-5
-4
-3
-2
-1
1
y
5

Consider the following graph:

a

Complete the table of values for the points shown on the line:

x-1012
y
b

State the values of the gradient m, and the y-intercept, c.

c

Hence write the equation for the line in gradient-intercept form.

d

Find the value of y when x = 19.

-4
-3
-2
-1
1
2
3
4
x
-7
-6
-5
-4
-3
-2
-1
1
2
3
y
6

Consider the following graph:

a

Complete the table of values for the points shown on the line:

x-50510
y
b

When x increases by 5, by how much does y increase?

c

Hence when x increases by 1, by how much does y increase?

d

State the values of the gradient m, and the y-intercept, c.

e

Hence write the equation for the line in gradient-intercept form.

f

Find the coordinates for the point on the line where x = 35.

-5
-4
-3
-2
-1
1
2
3
4
5
6
7
8
9
10
x
-5
-4
-3
-2
-1
1
2
3
y
7

Consider the following graph:

a

Complete the table of values for the points shown on the line:

x-50510
y
b

State the values of the gradient m, and the y-intercept, c.

c

Hence write the equation for the line in gradient-intercept form.

d

Find the coordinates for the point on the line where x = - 45.

-5
-4
-3
-2
-1
1
2
3
4
5
6
7
8
9
10
x
-2
-1
1
2
3
4
5
6
y
8

Consider the following graph:

a

Complete the table of values for the line shown in the graph:

x01
y
b

As x increases by 1, by how much does y increase?

c

State the values of the gradient m, and the y-intercept, c.

d

Hence write the equation of the line in gradient-intercept form.

e

Find the y-value of the point on the line where x = 22.

-5
-4
-3
-2
-1
1
2
3
4
5
x
-5
-4
-3
-2
-1
1
2
3
4
5
y
9

Consider the following graph:

a

Complete the table of values for the line shown in the graph:

x01
y
b

As x increases by 1, by how much does y decrease?

c

State the values of the gradient m, and the y-intercept, c.

d

Hence write the equation of the line in gradient-intercept form.

e

Find the y-value of the point on the line where x = 27.

-3
-2
-1
1
2
3
4
5
x
-6
-5
-4
-3
-2
-1
1
2
3
4
5
6
y
10

Consider the following graph:

a

As x increases by 1, by how much does y increase?

b

State the values of the gradient m, and the y-intercept, c.

c

Hence write the equation of the line in gradient-intercept form.

d

Find the coordinates for the point on the line where x = 50.

-3
-2
-1
1
2
3
x
-7
-6
-5
-4
-3
-2
-1
1
2
y
11

Consider the following graph:

a

As x increases by 2, by how much does y decrease?

b

Hence as x increases by 1, by how much does y decrease?

c

State the values of the gradient m, and the y-intercept, c.

d

Hence write the equation of the line in gradient-intercept form.

e

Find the coordinates for the point on the line where x = - 14.

-4
-3
-2
-1
1
2
3
4
x
-4
-3
-2
-1
1
2
3
4
y
12

For each of the following graphs:

i

State the coordinates of the y-intercept.

ii

Find the gradient of the line.

iii

Write the linear equation expressing the relationship between x and y in gradient-intercept form.

a
-5
-4
-3
-2
-1
1
2
3
4
5
x
-5
-4
-3
-2
-1
1
2
3
4
5
y
b
-5
-4
-3
-2
-1
1
2
3
4
5
x
-5
-4
-3
-2
-1
1
2
3
4
5
y
13

Find the equation expressing the relationship between x and y, in gradient-intercept form, for each of the following graphs:

a
-5
-4
-3
-2
-1
1
2
3
4
5
x
-5
-4
-3
-2
-1
1
2
3
4
5
y
b
-5
-4
-3
-2
-1
1
2
3
4
5
x
-5
-4
-3
-2
-1
1
2
3
4
5
y
14

Consider the following graph:

a

Find the linear equation expressing the relationship between x and y in gradient-intercept form.

b

Hence find the coordinates for the point on the line where x = 22.

-5
-4
-3
-2
-1
1
2
3
4
5
x
-5
-4
-3
-2
-1
1
2
3
4
5
y
15

Find the equation of the line in gradient-intercept form, given the following information:

a

The line has y-intercept of 4, and gradient of -3.

b

The line has y-intercept of -2, and gradient of 9.

c

The line contains the point \left(0,7\right) and has gradient of -1.

d

The line contains the origin and has gradient of \dfrac{3}{4}.

General form (Extended)
16

Rearrange the following linear equations into general form:

a
y = 5x - 9
b
y = 3x + 10
c
y = -7x
d
y = \dfrac{5}{2}x
e
y = \dfrac{6}{7}x -2
f
y = -\dfrac{5}{6}x + 3
g
y = 11 - \dfrac{1}{3}x
h
y = \dfrac{6}{5}x -7
17

For each of the following graphs:

i

State the coordinates of the y-intercept.

ii

Find the gradient of the line.

iii

Write the linear equation expressing the relationship between x and y in general form.

a
-5
-4
-3
-2
-1
1
2
3
4
5
x
-5
-4
-3
-2
-1
1
2
3
4
5
y
b
-5
-4
-3
-2
-1
1
2
3
4
5
x
-5
-4
-3
-2
-1
1
2
3
4
5
y
18

Consider the following graph:

a

Complete the table of values for the points shown on the line:

x-50510
y
b

State the values of the gradient m, and the y-intercept, c.

c

Find the equation of the line in general form.

d

Find the coordinates for the point on the line where x = 45.

-5
-4
-3
-2
-1
1
2
3
4
5
6
7
8
9
10
x
-6
-5
-4
-3
-2
-1
1
2
3
y
19

Find the equation expressing the relationship between x and y, in gradient-intercept form, for each of the following graphs:

a
-5
-4
-3
-2
-1
1
2
3
4
5
x
-5
-4
-3
-2
-1
1
2
3
4
5
y
b
-5
-4
-3
-2
-1
1
2
3
4
5
x
-5
-4
-3
-2
-1
1
2
3
4
5
y
20

Consider the following graph:

a

Find the linear equation in general form that expresses the relationship between x and y.

b

Find the coordinates for the point on the line where x = 25.

-5
-4
-3
-2
-1
1
2
3
4
5
x
-4
-3
-2
-1
1
2
3
4
y
21

Find the equation of the line in general form, given the following information:

a

The line contains the origin and the point \left(1,3\right).

b

The line contains the origin and the point \left(1,-5\right).

c

The line contains the points \left(0,-5\right) and \left(1,1\right).

d

The line contains the points \left(0,2\right) and \left(2,6\right).

Sign up to access Worksheet
Get full access to our content with a Mathspace account
Book a Demo
Sign up for free

Outcomes

0607E3.3

Determination of the value of at most two of a, b, c or d in simple linear, quadratic, cubic, reciprocal, exponential, absolute value and trignometric functions.

0607C4.6

Equation of a straight line as y = mx + c or x = k.

0607E4.6A

Equation of a straight line as y = mx + c.

What is Mathspace

About Mathspace