Topics
9. Linear Equations
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AustraliaAU
Year 11

9.06 Step graphs

Lesson
Worksheet
Practice
Worksheet
Interpret step graphs
1

The graph shows the amount (in dollars) an internet cafe charges its customers:

a

How much does Parvaneh have to pay if she uses their internet service for 2 hours and 40 minutes?

b

How much does Parvaneh have to pay if she uses their internet service for 4 hours?

c

What is the maximum number of hours that Parvaneh can use for \$15?

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\text{Hours}
5
10
15
20
\text{Cost}
2

The graph shows the starting times of a shot put event for participants of different age groups:

a

What time will a 13 year old participant start their race?

b

Do any of the races start at half past the hour?

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\text{Age}
4\text{ pm}
5\text{ pm}
6\text{ pm}
7\text{ pm}
8\text{ pm}
\text{Time}
3

The graph shows the amount (in dollars) a lawyer charges for consultations:

a

How much does the lawyer charge for a 5.5 hour consultation?

b

How much does the lawyer charge for a 4 hour consultation?

c

What is the shortest possible consultation that the lawyer will charge \$800 for?

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\text{Hours}
200
400
600
800
1000
1200
1400
1600
1800
2000
2200
2400
2600
\text{Cost}
4

The graph shows the cost (in dollars) of a mobile phone call as a function of the length of the call:

a

How much does a call that lasts 4 minutes and 5 seconds cost?

b

How much does a 3-minute call cost?

c

What is the longest possible call that could be made for \$1.50?

d

What is the cost of each additional minute?

e

What is the initial connection cost?

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\text{Minutes}
0.5
1
1.5
2
\text{Cost}
5

The graph shows the parking costs (in dollars) over different lengths of time:

a

How much would 5 hours of parking cost?

b

What is the longest you can park your car for \$6?

c

The carpark offers a weekly pass for \$44. If Aaron parks his car for 6 hours each day, five days a week, how much would he save each week with the weekly pass?

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\text{Hours}
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\text{Cost}
6

The step graph shows the cost (in dollars) for postage of packages based on their weight:

a

Find how much it will cost to post a package that weighs:

i

1.7\text{ kg}

ii

2.5\text{ kg}

iii

0.5\text{ kg}

iv

3.2\text{ kg}

b

If Neil has \$11, what range of package weights that he can afford to send?

c

What range of package weights can be sent for:

i
\$6
ii
\$7
iii
\$5.50
iv
\$14
0.5\text{kg}
1\text{kg}
1.5\text{kg}
2\text{kg}
2.5\text{kg}
3\text{kg}
3.5\text{kg}
4\text{kg}
\text{Weight}
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\text{Cost }
7

The cost (in dollars) of a train ticket, based on distance travelled (in km), is indicated by the step graph:

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\text{Distance}
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
5.5
\text{Cost}
a

If Valentina needed to travel a distance of 11\text{ km}, how much would her train ticket cost?

b

Luke has a doctor's appointment 19\text{ km} away. How much money will he need for a round-trip ticket?

c

Sally needs to travel 4 km to get to the grocery store. How much will a one way ticket cost?

d

With \$3, if Dave buys a round-trip ticket, he can travel no further than what distance?

e

Maria commutes approximately 40\text{ km} each direction every day to work. Calculate the total cost for one week's worth (five days) of round-trip tickets.

8

The graph shows the cost (in dollars) of sending parcels of various weights overseas:

a

Find the cost of sending a letter weighing 100 grams.

b

Find the cost of sending a letter weighing 300 grams.

c

What is the heaviest letter that can be sent for \$2?

50\text{ g}
100\text{ g}
150\text{ g}
200\text{ g}
250\text{ g}
300\text{ g}
\text{Weight}
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\text{Cost}
9

The graph shows the total cost of parking (in dollars) as a function of the number of hours parked:

a

How many free hours does this parking garage offer?

b

Peyvand goes to a movie and parks for 2.5 hours. How much will it cost her?

c

Tirdad works at the cinemas and parks for his entire 4.5-hour shift. How much will it cost him in parking?

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\text{Hours parked}
1
2
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5
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\text{Cost}
10

The graph shows the cost per t-shirt (in dollars) when purchasing in bulk:

a

What is the cost per t-shirt when 45 t-shirts are bought in bulk?

b

What is the cost per t-shirt when 55 t-shirts are bought in bulk?

c

What is the most number of t-shirts that can be purchased at \$7.00 each?

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\text{T-shirts}
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\text{Cost}
11

The step graph shows the charges (in dollars) for a home phone plan:

a

How much will a 3-minute phone call cost?

b

How much will 4 phone calls, each longer than 1 minute but less than 2 minutes, cost?

c

A phone line user made the following calls during one month:

  • 12 calls that were just under 2 minutes long each

  • 13 calls just under 4 minutes long each

  • 5 calls of less than 1 minute each

Find the total charges for the month to the nearest dollar.

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\text{Minutes}
0.3
0.6
0.9
1.2
1.5
1.8
2.1
2.4
2.7
3
\text{Cost}
Construct step graphs
12

Hiring helium tanks for balloons at a party costs \$20 up to and including the first hour, and \$5 per extra hour or any part thereof. Construct a step graph to represent the total cost for hiring helium tanks from 0 to 5 hours.

13

A telephone call is charged at \$0.70 for a call length of less than 1 minute, and \$0.20 extra per minute after that. Graph the cost of calls up to 5 minutes in length, with the vertical axis in dollars.

14

The cost of a train fare is calculated at \$1.30 for the first zone and then 20\text{c} per additional zone after that. Graph the fares for trips up to five zones, with the vertical axis in dollars.

15

A plumber charges a call-out fee of \$20 to come out to the site and on top of that, charges \$10 per 15-minute block on site or part thereof. Create a step graph that represents this scenario, with the vertical axis in dollars.

16

Create a step graph for the charge for sending parcels, where the vertical axis is in dollars:

Express Post satchels (mm)Maximum weight (g)Charge per item
\text{Small } (220 \times 355)500\$2.50
\text{Medium } (310\times405)3000\$4.25
\text{Large } (435\times510)5000\$7.75
17

A hotel charges the following rates for hiring out their function room:

  • \$160 per hour for up to 2 hours inclusive.

  • \$120 per hour for more than 2 hours and up to 5 hours inclusive.

  • \$80 per hour for more than 5 hours and up to 10 hours inclusive.

Create a step graph that shows the rate charged per hour for the length of time the function room is booked.

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Outcomes

ACMGM046

sketch piece-wise linear graphs and step graphs, using technology when appropriate

ACMGM047

interpret piece-wise linear and step graphs used to model practical situations; for example, the tax paid as income increases, the change in the level of water in a tank over time when water is drawn off at different intervals and for different periods of time, the charging scheme for sending parcels of different weights through the post

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