year 8 maths

444 Chapter 7 Linear relationships 1
Exercise 7H
EXTENSION
UNDERSTANDING AND FLUENCY
1–7 4–8
6–8
1 A rule linking distance d and time t is given by d = 10t + 5 . Use this rule to find the value of d for the
given values of t .
a t = 1 b t = 4 c t = 0 d t = 12
2 Write down the gradient ( m ) and the y -intercept ( b ) for these rules.
a y = 3x + 2 b y = −2x − 1 c y = 4x + 2
d y = −10x − 3 e y = −20x + 100 f y = 5x − 2
3 The height (in cm) of fluid in a flask increases at a rate of 30 cm every minute starting at 0 cm .
Find the height of fluid in the flask at these times.
a 2 minutes b 5 minutes c 11 minutes
4 The volume of gas in a tank decreases from 30 L by 2 L every second. Find the volume of gas in the
tank at these times.
a 1 second b 3 seconds c 10 seconds
Example 15
5 A jogger runs at a constant rate of 6 kilometres per hour for 3 hours.
a Draw a table of values, using t for time in hours and d for distance in kilometres.
Use t between 0 and 3 .
b Draw a graph by plotting the points given in the table in part a .
c Write a rule linking d with t .
d Use your rule to find the distance travelled for 1.5 hours of jogging.
e Use your rule to find how long it takes to travel 12 km .
6 A paddle steamer moves up the Murray River at a constant rate of 5 kilometres per hour for 8 hours.
a Draw a table of values, using t for time in hours and d for distance in kilometres. Use t between
0 and 8 .
b Draw a graph by plotting the points given in the table in part a .
c Write a rule linking d with t .
d Use your rule to find the distance travelled after 4.5 hours.
e Use your rule to find how long it takes to travel 20 km .
Example 16
7 The volume of water in a sink is 20 litres. The plug is pulled out and the volume decreases by
4 litres per second for 5 seconds.
a Draw a table of values, using t for time in seconds and V for volume in litres.
b Draw a graph by plotting the points given in the table in part a .
c Write a rule linking V with t .
d Use your rule to find the volume of water in the sink 2.2 seconds after the plug is pulled.
e Use your rule to find how long it takes for the volume to fall to 8 litres.
8 A weather balloon at a height of 500 metres starts to descend at a rate of 125 metres per minute for 4 minutes.
a Draw a table of values, using t for time in minutes and h for height in metres.
b Draw a graph by plotting the points given in the table in part a .
c Write a rule linking h with t .
d Use your rule to find the height of the balloon after 1.8 minutes.
e Use your rule to find how long it takes for the balloon to fall to a height of 125 metres .
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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