Topics
4. Linear relationships
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CanadaON
Grade 8

4.04 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 slope m, and the y-intercept, b.

c

Given that the linear relationship is in the form y = m x + b, 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 slope m, and the y-intercept, b.

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 slope m, and the y-intercept, b.

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 slope m, and the y-intercept, b.

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 slope m, and the y-intercept, b.

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 slope m, and the y-intercept, b.

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 slope m, and the y-intercept, b.

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 slope m, and the y-intercept, b.

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 slope m, and the y-intercept, b.

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 slope m, and the y-intercept, b.

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 slope m, and the y-intercept, b.

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 slope 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 slope of -3.

b

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

c

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

d

The line contains the origin and has slope 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).

18

Explain how to find the equation of the a line that passes through the points \left(0,2\right) and \left(2,6\right).

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Outcomes

8.B2.8

Compare proportional situations and determine unknown values in proportional situations, and apply proportional reasoning to solve problems in various contexts.

8.C1.1

Identify and compare a variety of repeating, growing, and shrinking patterns, including patterns found in real-life contexts, and compare linear growing and shrinking patterns on the basis of their constant rates and initial values.

8.C1.2

Create and translate repeating, growing, and shrinking patterns involving rational numbers using various representations, including algebraic expressions and equations for linear growing and shrinking patterns.

8.C4

Apply the process of mathematical modelling to represent, analyse, make predictions, and provide insight into real-life situations.

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