year 8 maths

7E
Gradient–intercept form
421
7E Gradient–intercept form
EXTENSION
From previous sections in this chapter you may have noticed some connections between the numbers that
make up a rule for a linear relationship and the numbers that are the gradient and y -coordinate with x = 0
(the y -intercept). This is no coincidence. Once the gradient and y -intercept of a graph are known, the rule
can be written down without further analysis.
Let’s start: What’s the connection?
To explore the connection between the rule for a linear relationship and the numbers that are the gradient
and the y -intercept, complete the missing details for the graph and table below.
5 (2, 5)
4
3 (1, 3)
2
1 (0, 1)
−4 −3 −2 −1
O
−1
1 2 3
(−1, −1)
−2
−3
y
x
x −1 0 1 2
y −1 1
+2
y = □ × x + □
Gradient = rise
run
= ___
y-intercept = ___
• What do you notice about the numbers in the rule, including the coefficient of x and the constant
(below the table), and the numbers for the gradient and y -intercept?
• Complete the details for this new example below to see if your observations are the same.
y
x −2 −1 0 1
−5
(−2, 3) 3
2
1
(−1, 0)
−4 −3 −2 −1
O
−1
−2
−3
−4
−5
−6
1 2 3
(0, −3)
(1, −6)
x
y
y = □ × x + □
Gradient = rise
run
= ___
y-intercept = ___
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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