year 8 maths

7H
Applying linear graphs
443
Example 16
Applying graphs when the rate is negative
The initial volume of water in a dish in the Sun is 300 mL . The water evaporates and the volume
decreases by 50 mL per hour for 6 hours.
a Draw a table of values, using t for time in hours and V for volume in millilitres.
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 dish after 4.2 hours in the Sun.
e Use your rule to find the time taken for the volume to reach 75 mL .
SOLUTION
a
t 0 1 2 3 4 5 6
V 300 250 200 150 100 50 0
EXPLANATION
The volume starts at 300 millilitres and decreases
by 50 millilitres every hour.
b
c
V (mL)
300
200
100
O
m = −50
1 = −50
1 2 3 4 5 6
t (hours)
b = 300
y = mx + b
V = −50t + 300
d V = −50t + 300
= −50 × 4.2 + 300
= 90
The volume of water in the dish is
90 millilitres after 4.2 hours.
e V = −50t + 300
75 = −50t + 300
−225 = −50t
4.5 = t
It takes 4.5 hours for the volume to
reach 75 mL .
Use numbers from 0 to 300 on the V -axis and
from 0 to 6 on the t -axis to accommodate all the
numbers in the table.
The gradient m in y = mx + b is given by
rise
run = −50
1 .
b is the y -intercept = 300
Substitute t = 4.2 into your rule to find V .
Substitute V = 75 into your rule.
Subtract 300 from both sides.
Divide both sides by −50 .
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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