year 8 maths

428 Chapter 7 Linear relationships 1
7F The x-intercept EXTENSION
We know that the y -intercept is determined by the point where a line cuts the y -axis. This is also the value
of y for the rule where x = 0 . Similarly, the x -intercept can be found by letting y = 0 . This can be viewed
in a table of values or found using the algebraic method.
y
x-intercept
where y = 0
x −3 −2 −1 0 1 2
y −1 0 1 2 3 4
y-intercept
where x = 0
4
3
x-intercept
2 y-intercept
1
−3 −2 −1
O
−1
1 2 3
−2
x
Let’s start: Discover the method
These rules all give graphs that have x -intercepts at which y = 0 .
A y = 2x − 2 B y = x − 5 C y = 3x − 9 D y = 4x + 3
• First try to guess the x -intercept using a trial and error (guess and check) method. Start by asking what
value of x makes y = 0 .
• Discuss why the rule for D is more difficult to work with than the others.
• Can you describe an algebraic method that will give the x -intercept for any rule? How would you
show your working for such a method?
Key ideas
■ The x -intercept is the x value of the point on a graph where y = 0 .
■ Find the x -intercept by substituting y = 0 into the rule. Solve the equation by inspection or
systematically. For example:
y = 2x + 4
−4
0 = 2x + 4
−4
−4 = 2x
÷2 −2 = x ÷2
y
4 (0, 4)
y-intercept = 4
∴ x -intercept is −2 .
x-intercept = −2
(−2, 0)
−2
O
x
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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