year 8 maths

7E
Gradient–intercept form
423
Example 8
Stating the gradient and y -intercept from the rule
Write down the gradient and y -intercept for the graphs of these rules.
a y = 2x + 3 b y = 1 3 x − 4
SOLUTION
a y = 2x + 3
gradient: m = 2
y -intercept: b = 3
b y = 1 3 x − 4
gradient: m = 1 3
y -intercept: b = −4
EXPLANATION
The coefficient of x is 2 and this number is the
gradient.
The y -intercept is the constant.
The gradient ( m ) is the coefficient of x.
Remember that y = 1 3 x − 4 is the same as y = 1 3 x + (−4)
so the constant is −4.
Example 9
Finding a rule from a graph
Find the rule for these graphs by first finding the values of m and the y -intercept.
a
y
b y
3 (1, 3)
2
1
−2 −1
O
−1
1 2
(0, −1)
−2
x
4 (0, 4)
3
2
1
(2, 0)
x
−1
O
−1
1 2
SOLUTION
a
m = rise
run
= 4 1 = 4
EXPLANATION
Between (0, −1) and (1, 3) the rise is 4 and the run is 1 .
b
b = −1
y = 4x − 1
m = rise
run
= −4
2
= −2
b = 4
y = −2x + 4
The line cuts the y -axis at −1 .
Substitute the value of m and b into y = mx + b .
Between (0, 4) and (2, 0) , y falls by 4 units as
x increases by 2 .
The line cuts the y -axis at 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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