year 8 maths

410 Chapter 7 Linear relationships 1
Key ideas
■ It is possible to use the table of values to express ‘the rule’ as an equation.
• The equations usually look like these:
y = 3x + 2 y = 3x − 1 y = 3x y = x + 3
■ If the numbers in the top row of the table are in sequence, the following hints make it simple to
find the equation.
+1 +1 +1 +1
x 0 1 2 3 4
y −1 3 7 11 15
+4 +4 +4 +4
• The numbers in the top row are increasing by 1 .
• The numbers in the bottom row are increasing by 4 .
• 4 divided by 1 gives 4 .
• The number in the bottom row under the 0 is −1 .
• The equation is y = 4x − 1 .
• In words, the rule is: To find the value of y , multiply x by 4 and then subtract 1 .
■ A rule must be true for every pair of numbers in the table of values. In the table above, if any
number in the top row is multiplied by 4 and then reduced by 1 , the result is the number below
it, in the bottom row.
• If the value of y when x = 0 is not given in the table, substitute another pair of coordinates
to find the value of the constant.
x 2 3 4 5
y 5 7 9 11
+2
+2
+2
y = 2x + □
5 = 2 × 2 + □ substituting (2, 5)
So □ = 1 .
Alternatively, extend the table to the left so that 0 appears in the top row.
x 0 1 2 3 4 5
y 1 3 5 7 9 11
−2 −2
■ The following names may be applied to the numbers in the equation.
y = 3 x + 2
coefficient of constant is 2
x is 3
■ In later sections, the coefficient of x is called the gradient.
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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