year 8 maths

7H
Applying linear graphs
441
7H Applying linear graphs
EXTENSION
Rules and graphs can be used to help analyse many situations in which there is a relationship between two
variables. If the rate of change of one variable with respect to another is constant, then the relationship
will be linear and a graph will give a straight line. For example, if a pile of dirt being emptied out of a pit
increases at a rate of 12 tonnes per hour, then the graph of the mass of dirt over time would be a straight
line. For every hour, the mass of dirt increases by 12 tonnes.
Let’s start: Water storage
The volume of water in a tank starts at 1000 litres and with constant rainfall the volume of water increases
by 2000 litres per hour for 5 hours.
• Describe the two related variables in this situation.
• Discuss whether or not the relationship between the two variables is linear.
• Use a table and a graph to illustrate the relationship.
• Find a rule that links the two variables and discuss how your rule might be used to find the volume of
water in the tank at a given time.
■ If the rate of change of one variable with respect
to another is constant, then the relationship
between the two variables is linear .
■ When applying straight-line graphs, choose letters
to replace x and y to suit the variables.
For example, V for volume and t for time.
■ y = mx + b can be used to help find the linear rule
linking two variables.
V (litres)
200
100
O
4
t (hours)
m = −25
b = 200
V = −25t + 200
Key ideas
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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