year 8 maths

422 Chapter 7 Linear relationships 1
Key ideas
■ The rule for a straight-line graph is given by y = mx + b or y = mx + c , where:
• m is the gradient
• b or c is the y -intercept
2
1
y
(1, 1)
−2 −1
O
−1
1 2
(0, −1)
−2
x
m =
2
= 2
1
b = −1
So y = mx + b becomes:
y = 2x − 1
■ A horizontal line (parallel to the x -axis) has the rule y = b or y = c .
Examples of horizontal lines include y = 5, y = −4 and y = 0 (which is the x -axis). They all
have zero gradient.
y
(0, 5)
y = 5
O
x
(0, −4)
y = −4
■ A vertical line (parallel to the y -axis) has the rule x = k .
Examples of vertical lines include x = 4, x = −2 and x = 0 (which is the y -axis). Their gradient
is undefined.
y
(−2, 0)
O
(4, 0)
x
x = −2
x = 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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