year 8 maths

634
7 a y = x + 2 b y = x − 4
c y = 2x − 1 d y = −x + 1
8 a y = 3x + 1. To find the number of matchsticks, multiply
the number of squares by 3 and then add 1.
b y = 5x + 1. To find the number of matchsticks, multiply
the number of hexagons by 5 and then add 1.
c y = 2x + 4. To find the number of matchsticks, multiply
the number in the top row by 2 and then add 4.
9 y = 8x − 2
10 y = −x + 1
11 a y = 5 − 2x b y = 7 − 3x
c y = 4 − x d y = 10 − 4x
12 a b − 2 b y = (b − 2)x + 2
13 a b − a b y = (b − a)x + a
14 a 5 extra matchsticks are needed for each new shape and
1 matchstick is needed for the first hexagon, so the rule
is y = 5x + 1.
b 2 extra matchsticks are needed for each new shape and
4 matchsticks are needed for the sides, so the rule is
y = 2x + 4.
15 a x is not increasing by 1. b 1 c y = x − 2
d i y = 2x + 3 ii y = 3x − 1
iii y = −2x + 3 iv y = −4x − 20
Exercise 7D
1 a positive b negative c negative d positive
2 a positive b undefined c zero d negative
3 a 2 b 3 c 3 2
d 2
13 a − 1 2
14 a 2 3
e − 3 7
i − 2 7
Exercise 7E
b − 3 2
b − 2 7
c b = − a 2
c 8 9
f 4 g − 8 9
j − 8 k − 18
33
25
d a = −2b
d 4 3
h −1
1 a y = 2x + 3 b y = 4x + 2 c y = −3x + 1
d y = −5x − 3 e y = 2x − 5 f y = −10x − 11
2 a b = 1, m = 2 b b = 0, m = 1 c b = −1, m = −1
d b = 3, m = −1 e b = 0, m = −3 f b = 3, m = 3
3 a m = 4, b = 2 b m = 3, b = 7
c m = 1 2 , b = 1 d m = 2 3 , b = 1 2
e m = −2, b = 3 f m = −4, b = 4
g m = −7, b = −1
h m = −3, b = −7
i m = −1, b = −6 j m = − 1 2 , b = 5
k m = − 2 3 , b = −1 2
l m = 3 7 , b = −4 5
4 a y = 2x − 1 b y = x − 2 c y = 3x + 3
d y = x + 5 e y = 2x + 1 f y = 3x − 1
5 a y = −x + 2 b y = −2x + 4 c y = −3x − 1
d y = −2x + 3 e y = −5x − 2 f y = −x + 6
6 a y = 4 b y = 1 c y = −3
d x = −4 e x = 5 f x = −2
7 a, b, c, d y
e −2 f −5 g − 8 3
h − 5 3
4 a 2 b 2 3
c −4 d − 2 5
e − 3 2
f − 1 2
g 1 2
h 3
5 a 3 b 1 c 1 2
(0, 5)
(0, 2)
(0, −1)
(0, −4)
y = 5
y = 2
x
y = −1
y = −4
d 3 e 2 3
f 4
e, f, g, h y
x = −1
6 a −2 b − 3 5
c − 4 3
d −1 e −3 f − 3 2
7 grassy slope
8 torpedo
9 a 3 4
b 5 2
c − 3 2
d − 7
10
(−3, 0)
x = −3
(−1, 0) (1, 0)
(4, 0)
x = 1
x = 4
x
10 a 5 2
b 5 3
c − 8 3
d − 2 e 8 f − 3
3
3
10
11 Answers may vary. Examples:
a (1, 3), (2, 6), (3, 9) b (−1, −3), (−2, −6), (−3, −9)
8 a y = 2 5 x + 2 b y = −1 4 x + 1 2
9 a y = 3x b y = −5x
c y = −x + 3 d y = 5 3 x − 4
c y = 1 3 x − 3 4
12 a 2 b 10 c b = 2a d a = b 2
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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