year 8 maths

7C
Finding the rule using a table of values
411
Example 4
Finding rules from tables
Find the rule for these tables of values.
a
x −2 −1 0 1 2
y −8 −5 −2 1 4
b
x 3 4 5 6 7
y −5 −7 −9 −11 −13
SOLUTION
a Coefficient of x is 3 .
Constant is −2 .
y = 3x − 2
b Coefficient of x is −2 .
y = −2x + □
Substitute (3, −5) .
−5 = −2 × 3 + □
−5 = −6 + □
So □ = 1 .
y = −2x + 1
EXPLANATION
x −2 −1 0 1 2
y −8 −5 −2 1 4
+3 +3 +3 +3
y = 3x − 2
x 3 4 5 6 7
y −5 −7 −9 −11 −13
−2 −2 −2 −2
y = −2x + □
To find the constant, substitute a point and choose the
constant so that the equation is true. This can be done
mentally.
Example 5
Finding a rule from a graph and write the rule in words
Find the rule for this graph by first constructing a table of (x, y) values. Write the rule in words.
y
3
2 (3, 1)
1
(2, 0)
−3 −2 −1
O
−1 1 2 3
(1, −1)
−2 (0, −2)
(−1, −3)
x
SOLUTION
x −1 0 1 2 3
y −3 −2 −1 0 1
Coefficient of x is 1 .
When x = 0, y = −2
y = x − 2
Rule in words: To find a y value, start with
x and then subtract 2 .
EXPLANATION
Construct a table using the points given on the graph.
Change in y is 1 for each increase by 1 in x .
x −1 0 1 2 3
y −3 −2 −1 0 1
+1 +1 +1 +1
y = 1x − 2 or y = x − 2
Cambridge Maths NSW
Stage 4 Year 8 Second edition
ISBN 978-1-108-46627-1 © Palmer et al. 2018
Cambridge University Press
Photocopying is restricted under law and this material must not be transferred to another party.