Chapter 4 Graphs in practical situations: Review
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Section 4A
1
Glen has started busking with his guitar to
make some extra cash. In the first month
he earned $48, in the second month he
earned $41, in the third month he earned
$63, and in the fourth month he earned
$54.
a
Complete the table using the values identified in the question.
Month
1
2
3
4
Earning
b
Plot the coordinates (Month, Earning) on a graph.
c
Join the coordinates in order of time.
d
Determine the month that Glen earned the most money.
e
Calculate the total Glen earned in the 4 months.
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Chapter 4 Graphs in practical situations: Review
Section 4B
2
Charlette sells jewellery at the local markets each week. In week 1 she made $112, in
week 2 she made $146, in week 3 she made $134, and in week 4 she made $121.
Enter Charlette’s income into a table of values and draw the graph. Calculate the
total Charlette made in the 4 weeks.
3
Jack is a pool cleaner and he charges a $20 call out fee and $38 per hour for
cleaning the pool. This can be mapped by the equation y = 38x + 20, where
x is the number of hours and y is Jack’s total fee.
x
0
1
2
3
y
a Complete the table of values for Jack’s fee.
b Determine after how many hours Jack has earned more than $100.
4
Fen won $2000 and spends $300 per week from her winnings until she has no money left.
This can be mapped by the equation y = 2000 − 300x, where x is the number of weeks and y
is the amount of money Fen has remaining. Complete the table of values for Fen’s
remaining winnings.
x
0
1
2
3
y
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Chapter 4 Graphs in practical situations: Review
5
Section 4C
6
Ian has purchased a mobile crane for $90 000. The crane depreciates (goes down in value)
by $12 500 per year and its value can be described as y = 90 000 − 12 500x, where y is the
crane’s value and x is the number of years.
a
Graph the equation of his crane’s value.
b
Determine after how many years the crane will be worth under $16 000.
Zac is a taxi driver who charges a $6.50 fee when picking up clients and then charges $0.90
per km travelled. The taxi fare can be described as y = 0.9x + 6.50, where y is the total taxi
fare and x is the number of kilometres travelled. If Zac picks up a client at Broome Airport
and takes them to the Broome Port Jetty, which is 8 km away, create a graph and determine
how much the total fare will be.
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Chapter 4 Graphs in practical situations: Review
Section 4D
7
Emma, who works at a café, gets paid according to how many hours she works in a week.
The table shows how much Emma is paid for a certain number of hours worked for that
week.
Hours
19
23
27
35
Pay ($)
342
414
486
630
a
Hand draw a line graph of this data, joining all points with a straight line.
b
Using the line graph, estimate how much Emma would get paid for working 30 hours
in a week.
c
Using the line graph, estimate how many hours Emma must work in order to earn $300
in a week.
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Chapter 4 Graphs in practical situations: Review
Section 4E
8
A veterinarian is putting together an informative chart for the dosage of medication
required for cats, depending on their weight, when rounded to the nearest kilogram. The
data that needs to be graphed is given below.
Cat’s weight (to the nearest kg)
Dosage of medicine (mL)
1
1.2
2
1.4
3
1.7
4
2.0
5
2.4
6
3.0
Using technology of your choice, use a spreadsheet to create a column graph of the data.
9
One of the responsibilities of Will, an aquaculture worker, is to monitor the condition
of the fish in a particular tank. Will has been instructed to turn off a water heater when
the water temperature rises above 25◦C. To monitor the temperature, there is a
graphical display showing the current temperature and a graph of how the temperature
has varied over the past 6 hours, as shown below.
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Chapter 4 Graphs in practical situations: Review
a
Estimate the temperature of the water in the tank at 10 a.m.
b
Estimate the temperature of the water in the tank at 11:30 a.m.
c At what time does the temperature of the water first rise above 25◦C?
d When does the graph suggest that Will has turned off the water heater? Justify your
response.
Section 4F
10 Frankie is on a direct train from Katherine to Alice
Springs and is travelling at a constant speed. The distance
from Alice Springs, in kilometres, against time, in hours,
is shown in the graph.
a
Approximately, how far from Alice Springs is Frankie
after 6 hours?
b
Approximately, how long does it take for Frankie to
be 400 km from Alice Springs?
c
Identify and interpret the vertical axis intercept.
d
Identify and interpret the horizontal axis intercept.
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Chapter 4 Graphs in practical situations: Review
11 A landscaper is installing an automated water system for
a client. As the length of hose increases, the water
pressure at each sprinkler decreases. The landscaper
graphs this relationship, as shown right, in order to
discuss it with the client.
a
What is the water pressure when 12 m of hose is
used?
b
What is the water pressure when 8 m of hose is
used?
c
The client does not wish the water pressure to drop below 30 psi. Up to what length of
hose does this allow the landscaper to install?
12 An accountant for a gym has been given the task of estimating the value of its range of
motion machine, depending on its age. The accountant gathers data on how the value of the
range of motion machine varies with age. The results are given in the table.
Age (years)
3
5
9
11
Value ($)
12 750
11 250
8250
6750
a
Using technology of your choice, use a spreadsheet to create a line graph of the data.
Display age on the horizontal axis, going from 0 to 25 years, and value on the vertical
axis, going from $0 to $20 000.
b
Using the line graph, estimate how much the range of motion machine is worth after 7
years.
c
Using the line graph, estimate after how many years the range of motion machine will
be worth $10 000.
d
State the value of the vertical axis intercept and interpret this value.
e
State the value of the horizontal axis intercept and interpret this value.
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Chapter 4 Graphs in practical situations: Review
13 A company that sells headphones will have a varying amount of profit, depending on how
many headphones it sells. The graph shows the revenue made (i.e. money made from
selling the headphones) in green and the expenses (i.e. how much it costs to make the
headphones) in red, against the number of headphones sold.
a
Approximate the profit/loss when the company sells 5 headphones.
b
Approximate the profit/loss when the company sells 25 headphones.
c
Identify and interpret the vertical axis intercept of the graph of expenses.
d
Identify and interpret the point of intersection.
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Chapter 4 Graphs in practical situations: Review
14 Both Lindsey and Josh have entered the
workforce with a sizeable debt from paying for
their education. They both pay off their debt in
regular payments until it is paid off. In order to
forecast how much they each have left to pay,
Josh creates the graph shown of how much they
each owe.
a
Approximately, how much does Josh have
left to pay after 10 years?
b
Approximately, how much does Lindsey
owe after 2 years?
c
Approximately, after how many years will Josh have just $10 000 owing?
d
Approximately, after how many years will Lindsey have just $16 000 left to pay?
e
Identify and interpret the vertical axis intercept for the graph of Josh’s debt.
f
Identify and interpret the vertical axis intercept for the graph of Lindsey’s debt.
g
Identify and interpret the horizontal axis intercept for the graph of Josh’s debt.
h
Identify and interpret the horizontal axis intercept for the graph of Lindsey’s debt.
i
Identify and interpret the point of intersection.
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