year 8 maths

7F
The x-intercept
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Example 11
Finding the x -intercept
For the graphs of these rules, find the x -intercept.
a y = 3x − 6 b y = −2x + 1
SOLUTION
a y = 3x − 6
+6
0 = 3x − 6
+6
6 = 3x
÷3 2 = x ÷3
∴ x -intercept is 2 .
EXPLANATION
Substitute y = 0 into the rule.
Add 6 to both sides.
Divide both sides by 3 .
b y = −2x + 1
−1
0 = −2x + 1
Substitute y = 0 into the rule.
−1
−1 = −2x
Subtract 1 from both sides.
÷2 1
2 = x
÷2
Divide both sides by −2 .
1
∴ x -intercept is
2 .
Example 12
Sketching with intercepts
Find the x - and y -intercepts and then sketch the graph of the rule y = 2x − 8 .
SOLUTION
y = 2x − 8
0 = 2x − 8
+8
8 = 2x
÷2 4 = x
+8
÷2
EXPLANATION
Substitute y = 0 into the rule.
Add 8 to both sides.
Divide both sides by 2 .
x-intercept is 4.
y-intercept is –8.
y
The y -intercept is the value of b in y = mx + b .
Alternatively, substitute x = 0 to get y = −8 .
Sketch by showing the x - and y -intercepts.
There is no need to show a grid.
O
4
x
−8
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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