year 8 maths

446 Chapter 7 Linear relationships 1
7I Non-linear graphs
Not all relationships between two variables are linear. The amount of money
invested in a compound interest account, for example, will not increase at a
constant rate. Over time, the account balance will increase more rapidly,
meaning that the graph of the relationship between Amount and Time will be
a curve and not a straight line.
Amount ($)
Let’s start: The fixed perimeter playpen
Time (years)
Imagine you have 10 metres of fencing material to make a rectangular playpen.
• List some possible dimensions of your rectangle.
• What is the area of the playpen for some of your listed dimensions?
• Complete this table, showing all the positive integer dimensions of the playpen.
Breadth (m) 1 2 3 4
Length (m) 3
Area (m 2 ) 6
• Plot the Area against Breadth to form a graph.
• Discuss the shape of your graph.
• Discuss the situation and graphical points when the breadth is
1 m or 4 m.
• What dimensions would deliver a maximum area and explain how
your graph helps determine this?
Area (m2)
7
6
5
4
3
2
1
O
1 2 3 4 5
Breadth (m)
Key ideas
■ To plot non-linear curves when given their rule, follow
these steps.
• Construct a table of values using the rule.
• Plot the points on a set of axes.
• Join the plotted points to form a smooth curve.
■ The graph of y = x 2 is an example of a non-linear graph
called a parabola .
The table shows five points that lie on the parabola. In each
point, the y value is the square of the x value.
x −2 −1 0 1 2
y 4 1 0 1 4
9
8
7
6
y = x 2
5
(−2, 4) 4 (2, 4)
3
2
(−1, 1) 1 (1, 1)
−3 −2 −1
O
−1
y
1 2 3
(0, 0)
x
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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