Topics
6 Linear relationships
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Stage 4

6.05 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 graph.

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 graph.

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 graph.

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 graph.

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 graph.

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 graph.

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 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 graph.

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
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 increase?

c

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

d

Hence write the equation of the line.

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
10

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.

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
11

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.

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
12

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.

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
13

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.

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
c
-5
-4
-3
-2
-1
1
2
3
4
5
x
-5
-4
-3
-2
-1
1
2
3
4
5
y
d
-5
-4
-3
-2
-1
1
2
3
4
5
x
-5
-4
-3
-2
-1
1
2
3
4
5
y
14

Find the equation expressing the relationship between x and y, 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
c
-5
-4
-3
-2
-1
1
2
3
4
5
x
-5
-4
-3
-2
-1
1
2
3
4
5
y
d
-5
-4
-3
-2
-1
1
2
3
4
5
x
-5
-4
-3
-2
-1
1
2
3
4
5
y
15

Consider the following graph:

a

Find the linear equation expressing the relationship between x and y.

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
16

Consider the following graph:

a

Find the linear equation expressing 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
17

Find the equation of the line, 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}.

e

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

f

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

g

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

h

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

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Outcomes

MA4-11NA

creates and displays number patterns; graphs and analyses linear relationships; and performs transformations on the Cartesian plane

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