18.05 Line graphs
This line graph shows the seal population at Rocky Point over a 5 year period:
Seal population at Rocky Point
What year had the lowest seal population?
One year, due to too much fishing in the local area, a shortage of fish caused the seal population to drop. In which year did the seal population drop?
What is the highest seal population over the five years?
By how much did the seal population increase over the five years?
The highest daily temperature in Sommersville over a week is shown in the line graph:
Which day had the warmest temperature?
Which two days had the same temperature?
How much warmer was Friday than Monday?
The line graph shows the number of ice creams sold at certain times of the day:
At what time of day were the least amount of ice creams sold?
What was the hightest amount of ice creams sold at a particular time?
There are two peak hours for ice cream sales, at lunch time (1 pm) and in the evening (6 pm). What was the difference in sales between these two peaks?
Danielle's distance from home throughout the day is recorded on the line graph:
How far was Danielle from her house at 2:00 pm?
What time did Danielle get back home?
What was the furthest distance Danielle was from her house?
Find the total time that Danielle was away from her house.
The line graph below shows the height of a tree over four years:
What is the initial height of the tree?
What is the height of the tree after 2.5 years?
Does the tree grow more in the first or the second year?
Find the total growth of the tree during the 4 years.
Fred ran in an obstacle course race with three laps. Each lap was divided into three equal sections. The time he took to complete each section of each lap in seconds, is represented in the line graph:
Find the time it took Fred to complete the first section of lap 2.
In which section of which lap did Fred have the fastest time?
Which two sections took Fred the same time?
What was the time difference in Fred completing section 2 of lap 3 compared to section 1 of lap 1?
The price of cans of soft drink over a year is shown on the line graph:
What was the lowest price of the cans of soft drink?
In which months was the price the lowest?
What was the highest price of the cans of soft drink?
In which months was the price the highest?
If 250 cans of soft drink are sold each month, calculate the difference in the value of the sales between the month with the highest price and the month with the lowest price.
Customers at Pareto's Burritos can select the hotness of their burritos on the Pareto Hotness Scale from \dfrac{0}{5} to \dfrac{5}{5}. The hotness that customers chose over a day is shown on the line graph:
Write the scores on the Pareto Hotness Scale in order from most popular to least popular.
How many more customers chose the most popular score than the second most popular score?
How many more customers chose the second least popular score than the least popular score?
How many more customers chose the most popular score than the least popular score?
How many customers participated in the survey?
Luigi brings a 1.8 \text{ L} bottle of water to work each day.
He records the amount of water in the bottle at the start of each hour on the line graph:
How much water was in Luigi's bottle at the start of the day?
What time was Luigi's bottle first refilled?
How much water did Luigi drink in the hour after first refilling his bottle?
How many hours were between the first and second time Luigi filled his bottle?
How much water did Luigi drink between the two refills?
How much did the amount of water in Luigi's bottle change between the start and end of the day?
How much did water did Luigi drink in total during the day?
The paper corporation records the amount of paper they produce each month over a year in the following line graph:
In which month did the paper corporation produce the most paper?
In which month did the paper corporation produce the least paper?
In which period did paper production increase the most?
In which period did paper production decrease the most?
In which period did paper production not change?
Sarah records her speed in metres per second at various points on a 1.5 \text{ km} running track on the following line graph:
At which three distances did Sarah reach a peak speed?
At which two distances did Sarah reach a trough speed (low point)?
How far did Sarah travel between the second trough and the third peak?
By how much did Sarah's speed increase between the second trough and the third peak?
The line graph shows the amount of petrol (in litres) in a car’s tank during a long drive:
Given that the drive started at 8 am:
How much petrol was initially in the tank?
What happened at 9 am and 1 pm?
Calculate the petrol used between 1 pm and 5 pm.
To the nearest hour, state the time the petrol in the tank first hit the 18 \text{ L} mark.
The line graph shows the temperature of a cup of tea in degrees Celsius over a twenty minute time period:
State the temperature after the cup of tea has been left to cool for 10 minutes.
Does the temperature of the cup of tea drop more in the first 5 minutes or the last 5 minutes?
Calculate the overall drop in temperature during the 20 minutes.
The graph represents the number of iTunes sales (in millions) and iPod sales (in hundreds of thousands) every 3 months between 2003 and 2007:
State the number of iTunes sales for the first quarter of 2006.
State the number of iPod sales for the first quarter of 2006.
How many more iTunes sales were there than iPod sales in the first quarter of 2007?
Calcuate the total number of iTunes sales in 2006.
The graph below shows the median house prices per quarter for the four years to September 2013:
Describe the underlying trend in median house prices over the four years.
Find the range of prices over the four year period to the nearest \$100\,000.
List the quarters in which the three highest median house prices occurred.
The graph given shows monthly rainfall data for Berlin and London:
Which city records the highest monthly rainfall over the year?
Calculate the range in monthly rainfall for Berlin between June and October.
In the months between March and July (inclusive), find the range in London's monthly rainfall.
Which city has the lowest range over the year?
In which month did the cities have the smallest difference in rainfall?
The table shows the number of different vegetables Susana ate on each day of the week. Construct a line graph for this information.
| Day | \text{Sun} | \text{Mon} | \text{Tue} | \text{Wed} | \text{Thu} | \text{Fri} | \text{Sat} |
|---|---|---|---|---|---|---|---|
| No. of Vegetables | 4 | 6 | 1 | 1 | 3 | 2 | 5 |
Dylan writes a new song and asks his friends to give it a score from 0 to 1. Construct a line graph for this information.
| Score | 0.0 | 0.1 | 0.2 | 0.3 | 0.4 | 0.5 | 0.6 | 0.7 | 0.8 | 0.9 | 1.0 |
|---|---|---|---|---|---|---|---|---|---|---|---|
| Number | 8 | 3 | 8 | 5 | 6 | 9 | 10 | 9 | 9 | 8 | 9 |
A kitchen sink starts with 20 \text{ L} of water in it. It empties at a rate of 4 \text{ L} per minute and then after 4 minutes the drain gets blocked. No water empties for 2 more minutes while it gets unblocked and then the remaining water is drained out in 1 minute.
Construct a line graph that represents this scenario.
A tank is being filled at a constant rate of 4 \text{ L} per second for 4 minutes. The hose is then turned off for 2 minutes. Finally it is topped up again with water at a rate of 3 \text{ L} per second for 1 minute.
Construct a line graph that represents this scenario.
The following table shows the maximum temperature reached each day of the week in a city:
| \text{Day} | \text{Mon} | \text{Tue} | \text{Wed} | \text{Thu} | \text{Fri} | \text{Sat} | \text{Sun} |
|---|---|---|---|---|---|---|---|
| \text{Temperature} \left(\degree C\right) | 20 | 22 | 24 | 19 | 18 | 17 | 18 |
Plot a time series graph for the data.
Which day had the greatest maximum temperature?
What was the largest drop in temperature?
The following table shows the Australian mean monthly rainfall for 2018:
Plot a time series graph for the data.
Which month was the driest?
Which month had the largest average rainfall?
Is the average rainfall for January higher or lower than the sum of the average rainfall over the winter months?
| \text{Month} | \text{Rainfall (mm)} |
|---|---|
| \text{Jan} | 105 |
| \text{Feb} | 75 |
| \text{Mar} | 60 |
| \text{Apr} | 10 |
| \text{May} | 10 |
| \text{Jun} | 20 |
| \text{Jul} | 10 |
| \text{Aug} | 15 |
| \text{Sep} | 5 |
| \text{Oct} | 25 |
| \text{Nov} | 35 |
| \text{Dec} | 40 |
The following table shows the average daily maximum temperature for Perth in 2018:
Plot a time series graph for the data.
Which month had the largest average daily maximum temperature?
What is the difference between the highest and lowest average daily maximum temperature?
| \text{Month} | \text{Temperature } \left(\degree C\right) |
|---|---|
| \text{Jan} | 31 |
| \text{Feb} | 32 |
| \text{Mar} | 30 |
| \text{Apr} | 26 |
| \text{May} | 22 |
| \text{Jun} | 20 |
| \text{Jul} | 18 |
| \text{Aug} | 19 |
| \text{Sep} | 20 |
| \text{Oct} | 23 |
| \text{Nov} | 27 |
| \text{Dec} | 29 |
The following table shows the UV rating for a summer’s day in Sydney:
| Time (in 24 hours) | 0600 | 0800 | 1000 | 1200 | 1400 | 1600 | 1800 |
|---|---|---|---|---|---|---|---|
| UV index | 0 | 0.9 | 6.3 | 10.5 | 11.7 | 7.2 | 2.4 |
Plot a time series graph for the data.
At approximately what time was the UV index the highest?
A very high rating is considered to be 7.2 or above. For approximately which range of hours should a person stay inside to avoid being in the sun above this UV index?
The following table shows the sales in thousands of dollars for a particular company:
| Year | 2010 | 2011 | 2012 | 2013 | 2014 | 2015 | 2016 |
|---|---|---|---|---|---|---|---|
| Profit (in thousands of dollars) | 55 | 62 | 60 | 58 | 64 | 76 | 83 |
Plot a time series graph for the data.
Describe the underlying trend of the data.
Find the percentage growth in profit from 2010 to 2016. Round your answer to the nearest percent.
The following table shows the sales (in thousands of items) for a particular product of a company:
Plot a time series graph for the data.
What is the general trend in the monthly sales?
What is the percentage decrease in sales from January to December?
| Month | Sales (in thousands) |
|---|---|
| \text{Jan} | 5.0 |
| \text{Feb} | 4.5 |
| \text{Mar} | 3.5 |
| \text{Apr} | 4.0 |
| \text{May} | 2.5 |
| \text{Jun} | 3.0 |
| \text{Jul} | 2.5 |
| \text{Aug} | 2.0 |
| \text{Sep} | 1.5 |
| \text{Oct} | 2.0 |
| \text{Nov} | 1.5 |
| \text{Dec} | 2.0 |
The following table shows the share price for a company's stock at the end of each month:
Plot a time series graph for the data.
Which month saw the sharpest drop in stock price?
What was the loss per share from the January price to the December price, in dollars?
Is the trend in the stock price generally increasing, generally decreasing, or generally centred around a constant?
| \text{Month} | \text{Share price }(\$) |
|---|---|
| \text{Jan} | 8.5 |
| \text{Feb} | 9.35 |
| \text{Mar} | 9.95 |
| \text{Apr} | 9.20 |
| \text{May} | 9.80 |
| \text{Jun} | 8.15 |
| \text{Jul} | 8.25 |
| \text{Aug} | 8.90 |
| \text{Sep} | 8.60 |
| \text{Oct} | 8.40 |
| \text{Nov} | 8.30 |
| \text{Dec} | 8.0 |
The following table shows the number of passengers at a train station over a day:
| Time (in 24 hours) | 0600 | 0800 | 1000 | 1200 | 1400 | 1600 | 1800 | 2000 | 2200 |
|---|---|---|---|---|---|---|---|---|---|
| Number of passengers | 100 | 400 | 180 | 270 | 290 | 90 | 360 | 140 | 80 |
Plot a time series graph for the data.
How many times more passengers are there at the station during the morning peak time compared to the lowest number of passengers recorded?
The following table shows the average fuel price for each day of the week in the city:
| Day | \text{Mon} | \text{Tue} | \text{Wed} | \text{Thu} | \text{Fri} | \text{Sat} | \text{Sun} |
|---|---|---|---|---|---|---|---|
| Price (in dollars) | 1.40 | 1.42 | 1.38 | 1.40 | 1.46 | 1.42 | 1.44 |
Plot a time series graph for the data.
Which was the best day to buy fuel and what was the average cost on this day?
On which days was the average fuel price \$1.40?
By what percentage did the price change from Monday to Friday?
The local police station records the number of speeding fines issued each quarter. The following table has the data for each quarter from 2012 to 2014:
| Period | Time | Number of speeding fines | Percentage of yearly mean |
|---|---|---|---|
| 1 | \text{March 2012} | 20 | 83.33\% |
| 2 | \text{June 2012} | 28 | 116.67\% |
| 3 | \text{September 2012} | 36 | 150\% |
| 4 | \text{December 2012} | 12 | 50\% |
| 5 | \text{March 2013} | 24 | 81.36\% |
| 6 | \text{June 2013} | 35 | 118.64\% |
| 7 | \text{September 2013} | 42 | 142.37\% |
| 8 | \text{December 2013} | 17 | 57.63\% |
| 9 | \text{March 2014} | 32 | 89.51\% |
| 10 | \text{June 2014} | 39 | 109.09\% |
| 11 | \text{September 2014} | 51 | 142.66\% |
| 12 | \text{December 2014} | 21 | 58.74\% |
Plot a time series graph for the number of fines recorded each quarter against the period.
Describe the underlying trend of the data.
From the beginning of 2012, the number of new houses built in the suburb of Woodford was recorded and figures are released every four months.
The table shows the data from the beginning of 2012 to the end of 2015:
Plot a time series graph for the data.
Which month appears to be the peak season for new houses?
Describe the overall underlying trend of the data.
| Time period | Houses built |
|---|---|
| \text{April }2012 | 103 |
| \text{August }2012 | 92 |
| \text{December }2012 | 105 |
| \text{April }2013 | 99 |
| \text{August }2013 | 88 |
| \text{December }2013 | 104 |
| \text{April }2014 | 93 |
| \text{August }2014 | 85 |
| \text{December }2014 | 103 |
| \text{April }2015 | 93 |
| \text{August }2015 | 83 |
| \text{December } 2015 | 96 |
The graph shows the conversion between temperatures in Celsius and Fahrenheit:
Use the graph to convert 10 \degree \text{C} into Fahrenheit.
0 \degree \text{C} is 32 \degree \text{F}. Hence, for every 1 \degree \text{C} increase, by how much does the Fahrenheit temperature increase?
Would 80 \degree \text{F} be above or below normal body temperature (approximately 37 \degree \text{C})?
Write the rule for conversion between Celsius \left(\text{C}\right) and Fahrenheit \left(\text{F}\right).
Convert 35 \degree \text{C} into Fahrenheit.
Use the given graph to convert the following:
Convert 0 \degree \text{F} to Celcius.
Convert 40 \degree \text{C} to Fahrenheit.
Convert - 20 \degree \text{F} to Celsius.
Convert 60 \degree \text{F} to Celcius.
The graph shows the amount of Euros that can be bought with Australian Dollars on a particular date:
How many Euros can \$20 AUD buy?
How much Australian currency is required to buy 6 Euros?
Calculate the number of Euros that \\ \$1 AUD buys.
Consider the following graph which relates the two units, pounds and kilograms.
Convert 10 \text{ kg} to pounds.
Convert 44 \text{ lb} to kilograms.
A casserole recipe calls for one pound of vegetables. How much is this in kilograms?
Consider the following graph which relates the two units, miles per hour and kilometres per hour.
Convert 50 \text{ mi/h} to \text{km/h}.
Lachlan has a classic car which still has gauges with units in \text{mi/h}. If he drives down a road with a limit of 80 \text{ km/h} , what is the highest speed he can drive in \text{mi/h}?
What fraction must you multiply by to convert \text{km/h} to \text{mi/h}?
The graph shows the conversion between Country A and Country B's currency:
Use the graph to convert 8 of currency A to currency B.
Use the graph to convert 2 of currency B to currency A.
Consider the following graph which relates the two units, millilitres and cups.
A recipe calls for 750 \text{ mL} of milk, how many cups is this?
How many millilitres are there in one cup?
If a litre of vegetable stock is required for a recipe, how many cups is this?
Consider the following graph which relates the two units, US dollars and Australian dollars:
An item online costs \$18 USD. Approximately, what is the cost in AUD?
How many USD can be purchased with \$58 AUD?
What is the exchange rate to convert AUD to USD?
Consider the following graph which relates Indonesian rupiah and Australian dollars:
If Holly goes on holiday to Bali and spends 50\,000 IDR per day on food for 4 days, how much AUD would this be in total?
How many rupiahs would \$50 AUD buy?
What is the exchange rate to convert AUD to INR?
Consider the following graph which relates the two units, Kilojoules and Calories.
From the graph, convert 50 \text{ Cal} to kilojoules.
Give your answer to the nearest 100 \text{ kJ}.
From the graph, convert 400 \text{ kJ} to Calories.
Give your answer to the nearest 10 \text{ Cal}.
If two chocolate biscuits are 90 Calories each, approximately how many kilojoules is this?
Give your answer to the nearest 100 \text{ kJ}.
Consider the following graph which relates the two units, litres and gallons.
Convert 10 \text{ gal} to litres.
Convert 60 \text{ L} to gallons.
If a typical small car in the US has a fuel tank that holds 12 gallons, how many litres is this roughly?
The graph shows the cost of sending parcels of various weight overseas:
Find the cost of sending a letter weighing:
100 \text{ g}
300 \text{ g}
125 \text{ g}
Find the heaviest letter that can be sent for \$2.
Write an inequality for the range of letter weights that can be sent for \$4.
The graph shows the parking costs over different lengths of time:
Calculate the cost of 5 hours of parking.
Determine the longest time you can park your car for \$6.
The carpark offers a weekly pass for \$44. If Aaron parks his car for 6 hours each day, five days a week, how much does he save each week with the weekly pass?
The graph shows the amount (in dollars) an internet cafe charges its customers:
How much does a customer have to pay if they use the internet service for 2 hours and 40 minutes?
How much does a customer have to pay if they use the internet service for 4 hours?
Find the maximum number of hours that a customer can purchase for \$15.
The graph shows the starting times of a shot put event for participants of different age groups:
Determine the time a participant who is aged 7 will start their event.
Determine the time a participant who is aged 13 will start their event.
Determine the time a participant who is aged 16 will start their event.
Do any of the events start at half past the hour?
The graph shows the total cost of parking (in dollars) as a function of the number of hours parked:
Calculate the number of free hours this parking garage offers.
Janet goes to a movie and parks for 2.5 hours. How much will it cost her?
Connor works at the cinemas and parks for his entire 4.5 hour shift. How much will it cost him in parking?
The graph shows the amount (in dollars) a lawyer charges for consultations:
How much does the lawyer charge for a 3 hour consultation?
How much does the lawyer charge for a 5.5 hour consultation?
How much does the lawyer charge for a 4 hour consultation?
Determine the shortest possible consultation time for which the lawyer will charge \$800.
The graph shows the cost per t-shirt (in dollars) when purchasing in bulk:
Find the cost per t-shirt when 45 t-shirts are bought in bulk.
Find the cost per t-shirt when 55 t-shirts are bought in bulk.
Find the maximum number of t-shirts that can be purchased at \$7.00 each.
The graph shows the cost (in dollars) of a mobile phone call as a function of the length of the call:
Find the cost of a 4 minute and 5 second call.
Find the cost of a 3 minute call.
Find the longest possible call that could be made for \$1.50.
Find the cost of each additional minute.
Calculate the connection cost.
The step graph shows the cost (in dollars) for postage of packages based on their weight:
Find how much it will cost to post a package that weighs:
1.7\text{ kg}
2.5\text{ kg}
0.5\text{ kg}
3.2\text{ kg}
If Neil has \$11, what range of package weights that he can afford to send?
What range of package weights can be sent for:
The cost of a train ticket, based on distance travelled, is indicated by the step graph:
If Valentina needs to travel a distance of 11\text{ km}, how much does her train ticket cost?
Luke has a doctor's appointment 19\text{ km} away. Calculate the cost of a round-trip ticket.
Sally needs to travel 4\text{ km} to get to the grocery store. Calculate the cost of a one way ticket.
With \$3, if Dave buys a round-trip ticket, what is the maximum distance he can travel?
Maria commutes approximately 40\text{ km} each direction every weekday to work. Calculate her weekly work commuting cost.
The step graph shows the charges for a home phone plan:
How much will a 3 minute phone call cost?
Calculate the cost of 4 phone calls, each longer than 1 minute but less than 2 minutes.
A phone line user made 12 calls that were just under 2 minutes long each, 13 calls just under 4 minutes long each, and 5 calls of less than 1 minute each. Calculate the total cost for the calls.
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. Create a step graph that shows the cost of calls up to 5 minutes in length.
The cost of a train fare is calculated at \$1.30 for the first zone and then 20 cents per additional zone after that. Create a step graph that shows the fares for trips up to five zones.
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.
Create a step graph displaying the total cost of hiring helium tanks for up to five hours.
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 matches this scenario.
Consider the following table and create a step graph for the charge for sending parcels:
| \text{Express Post satchels (mm)} | \text{Maximum weight (g)} | \text{Charge per item} |
|---|---|---|
| \text{Small } (220\times 355) | 500 | \$2.50 |
| \text{Medium } (310\times 405) | 3000 | \$4.25 |
| \text{Large } (435\times 510) | 5000 | \$7.75 |
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 amount charged per hour for the length of time the function room is booked.
At an indoor ski facility, the temperature is set to - 5 \degree \text{C} at 2 pm. At 3 pm, the temperature is immediately brought down to - 12 \degree \text{C} and left for 3 hours before immediately taking it down again to - 18 \degree \text{C}, where it stays for the rest of the day’s operation. The facility operates until 10 pm.
Complete the stepwise function that models the indoor temperature, y, at a certain time of the day, x hours after midday:
y = \begin{cases} -5\degree \text{C}, & ⬚ \leq x \lt 3 \\ ⬚\degree \text{C}, & 3 \leq x \lt 6 \\ ⬚\degree \text{C}, & 6 \leq x \leq ⬚ \end{cases}Create a graph of the step function.
Lakota entered the ski facility at 3:30 pm. What was the temperature inside the facility at this time?
Xavier wants to wait till the indoor temperature is - 7 \degree \text{C} or lower. When is the earliest he can enter the facility?