year 8 maths

406 Chapter 7 Linear relationships 1
Example 2
Plotting a graph from a rule
For the rule y = 2x − 1 construct a table and draw a graph.
SOLUTION
x −3 −2 −1 0 1 2 3
y −7 −5 −3 −1 1 3 5
5
4
3
2
1
−3 −2 −1
O
−1
−2
(−1, −3) −3
−4
(−2, −5) −5
−6
(−3, −7) −7
y
(1, 1)
(2, 3)
1 2 3
(0, −1)
(3, 5)
x
EXPLANATION
Substitute each x -coordinate in the table into the
rule to find the y -coordinate.
Plot each point (−3, −7), (−2, −5) … and join
them to form the straight-line graph.
Example 3
Checking if a point lies on a line
Decide if the points (1, 3) and (−2, −4) lie on the graph of y = 3x .
SOLUTION
Substitute (1, 3) .
y = 3x
LHS = y RHS = 3x
= 3 = 3 × 1
= 3
LHS = RHS
So (1, 3) is on the line.
Substitute (−2, −4) .
y = 3x
LHS = y RHS = 3x
=−4 = 3 ×−2
=−6
LHS ≠ RHS
So (−2, −4) is not on the line.
EXPLANATION
Substitute (1, 3) into the rule for the line.
The point satisfies the equation, so the point is on
the line.
Substitute (−2, −4) into the rule for the line.
The point does not satisfy the equation, so the point
is not on the line.
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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