year 8 maths

416 Chapter 7 Linear relationships 1
Example 6
Defining a type of gradient
Decide if the lines labelled a , b , c and d on this graph have a positive, negative, zero or undefined
gradient.
y
d
c
x
a
b
SOLUTION
EXPLANATION
a negative gradient As x increases, y decreases.
b undefined gradient
The line is vertical.
c positive gradient y increases as x increases.
d zero gradient
There is no increase or decrease in y as x increases.
Example 7
Finding the gradient from a graph
Find the gradient of these lines.
a
y
3
2
1
O
1 2
(2, 3)
x
b
y
4 (0, 4)
3
2
1
(4, 0)
x
−1
O
−1
1 2 3 4
SOLUTION
a
EXPLANATION
Gradient = rise
The rise is 3 for every 2
run
= 3 across to the right.
2 or 1.5
b Gradient = rise
run
= −4
4
= −1
The y value falls 4 units
while the x value increases
by 4 .
Run = 2
Run = 4
Rise = 3
Rise = −4
Cambridge Maths NSW
Stage 4 Year 8 Second edition
ISBN 978-1-108-46627-1 © Palmer et al. 2018
Cambridge University Press
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