year 8 maths

7E
Gradient–intercept form
427
13 Write the rule for these graphs. Your rule could include the pronumerals a and/or b .
a
y
b
y
(a, b)
O
x
O
x
(a, −a)
c
y
(0, a)
O
(b, 0)
x
14 Some rules for straight lines may not be written in the form y = mx + b . The rule 2y + 4x = 6 , for
example, can be rearranged to 2y = −4x + 6 and then to y = −2x + 3 . So m = −2 and b = 3 . Use this
idea to find m and b for these rules.
a 2y + 6x = 10 b 3y − 6x = 9 c 2y − 3x = 8 d x − 2y = −6
ENRICHMENT
– –
15
Sketching with m and b
15 The gradient and y -intercept can be used to sketch a graph without the need to plot more than two points.
For example, the graph of the rule y = 2x − 1 has m = 2 = 2 and b = −1 . By plotting the point
( 1)
(0, −1) for the y -intercept and moving 1 to the right and 2 up for the gradient, a second point (1, 1)
can be found.
y
2
1
(1, 1)
−1
O
−1
1 2
(0, −1)
x
Use this idea to sketch the graphs of these rules.
a y = 3x − 1 b y = 2x − 3 c y = −x + 2 d y = −3x − 1
e y = 4x f y = −5x g y = 1 2 x − 2 h y = −3 2 x + 1
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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