A dam used to supply water to the neighboring town had the following data recorded for its volume over a number of months:
| \text{Month }(M) | 1 | 2 | 3 | 4 |
|---|---|---|---|---|
| \text{Volume in billions of litres } (V) | 112 | 106 | 110 | 80 |
Plot the points on the number plane.
Is this relationship linear?
Chirping crickets can be used as an indication of how hot or cool it is outside. Different species of crickets have different chirping rates but for a particular species the following data was recorded:
| \text{Number of chirps per minute } (x) | 80 | 110 | 140 | 160 |
|---|---|---|---|---|
| \text{Temperature } (y \ \degree \text{C}) | 16 | 19 | 22 | 24 |
Graph the linear relationship represented in the table.
Determine the temperature when the crickets make 130 chirps each minute.
How many chirps per minute will the crickets make if the temperature is 27\degree\text{C}?
How many chirps per minute will the crickets make if the temperature is 20\degree\text{C}?
A diver starts at the surface of the water and begins to descend below the surface at a constant rate. The table below shows the depth of the diver over 4 minutes:
| \text{Number of minutes passed } (x) | 0 | 1 | 2 | 3 | 4 |
|---|---|---|---|---|---|
| \text{Depth of diver in metres } (y) | 0 | 0.8 | 1.6 | 2.4 | 3.2 |
Graph the linear relationship represented in the table.
Calculate the increase in depth each minute.
Calculate the depth of the diver after 24 minutes.
Petrol costs a certain amount per litre. The table shows the cost of various amounts of petrol in dollars:
| \text{Number of litres }(x) | 0 | 10 | 20 | 30 | 40 |
|---|---|---|---|---|---|
| \text{Cost of petrol }(y) | 0 | 16.40 | 32.80 | 49.20 | 65.60 |
Find the cost of petrol per litre.
Write an equation linking the number of litres of petrol pumped \left(x\right) and the cost of the petrol \left(y\right).
Explain the meaning of the gradient in this context.
Calculate the cost of 47 \text{ L} petrol.
The time in minutes and the temperature in degrees Celsius (\degree \text{C}) are given in the following table:
| \text{Time } (x) | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|
| \text{Temperature } (y\degree \text{C}) | 8 | 13 | 18 | 23 | 28 |
By how much is the temperature increasing each minute?
Find the initial temperature.
Form an equation relating x and y.
Graph the linear relationship represented in the table.
Petrol costs a certain amount per litre. The table shows the cost of various amounts of petrol in dollars:
| \text{Number of litres }(x) | 0 | 10 | 20 | 30 | 40 |
|---|---|---|---|---|---|
| \text{Cost of petrol }(y) | 0 | 12 | 24 | 36 | 48 |
Graph the linear relationship represented in the table.
Find the cost of petrol per litre.
Calculate the cost of 75 \text{ L} petrol.
Consider the following table that shows the temperature of a metal plate, in \degreeC, after an amount of time, measured in minutes:
| \text{Time }(x) | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|
| \text{Temperature }(y) | 10 | 15 | 20 | 25 | 30 |
Graph the linear relationship represented in the table.
By how much is the temperature increasing each minute?
Find the initial temperature.
Form an equation relating x and y.
After Sally starts running, her heartbeat increases at a constant rate as shown the following table:
| \text{Number of minutes passed } (x) | 0 | 2 | 4 | 6 | 8 | 10 | 11 |
|---|---|---|---|---|---|---|---|
| \text{Heart rate } (y) | 75 | 81 | 87 | 93 | 99 | 105 |
Complete the table.
Graph the linear relationship represented in the table.
By how much is her heartbeat increasing each minute?
Emma is gathering data on the growth of her plant as shown in the following table:
| \text{Day } (d) | 2 | 4 | 6 | 8 |
|---|---|---|---|---|
| \text{Height of plant } (h \text{ cm}) | 6 | 10 | 14 | 18 |
Graph the linear relationship represented in the table.
How tall was the plant when Emma started tracking the growth?
Determine the height of the plant on day 12.
On which day will the plant be 18 \text{ cm} tall?
Write a linear equation to represent the height, h, as a function of the day, d.
When a plane is coming in to land, the pilot requires the plane to lose altitude at a rate of 5\text{ m/s}. At the beginning of a particular descent the plane starts at an altitude of 8500\text{ m}. The altitude of the plane at various times since starting descent are shown in the following table:
| \text{Descent } (t\text{ seconds}) | 0 | 200 | 400 | 1600 |
|---|---|---|---|---|
| \text{ Altitude } (A) | 8500 | 7500 | 6500 | 500 |
Graph the linear relationship represented in the table.
Determine the altitude of the plane 500 seconds since starting the descent.
How many seconds did the plane take to descend to the ground?
Write a linear equation to represent the altitude of the plane, A, as a function of the number of seconds since commencing descent, t.
Katrina is going to catch a taxi into the city. She knows that the taxi has a flat fee of \$0.30 and that the fare rises by \$0.10 per kilometre travelled. The fares for particular distances are shown in the following table:
| \text{Distance travelled } (d \text { km}) | 6 | 7 | 8 | 9 |
|---|---|---|---|---|
| \text{Fare } (F) | 0.90 | 1.00 | 1.10 | 1.20 |
Graph the linear relationship represented in the table.
Write a linear equation to represent the fare, F, as a function of the journey's length, d.
Calculate the fare for a 14 \text{ km} journey.
Find the distance travelled for a trip that costs \$0.60.
Justin is looking into the details of his mobile phone plan. He knows the costs for several call lengths as shown in the table:
| \text{Length of call in minutes } (t) | 2 | 6 | 10 | 14 |
|---|---|---|---|---|
| \text{Cost } (C) | \$1.00 | \$2.20 | \$3.40 | \$4.60 |
Plot the given data on a number plane and connect the points with a line.
How much will it cost to make an 8-minute call?
Find the length of a call that costs \$1.60.
Determine the rule that connects the cost of a call, C, to the length of the call, t.
Beth’s income is based solely on the number of hours she works, and she is paid a fixed hourly wage. She earns \$750 for working 30 hours. Let y represent Beth’s income after working x hours.
Sketch a graph that displays her income against her hours worked.
Form an equation relating x and y.
Calculate Beth's income when she works 25 hours.
Calculate the number of hours that Beth must work to earn \$125.
The cost, y, for a business to operate, can be expressed in terms of x, the total number of hours it has operated for. The cost is \$150 an hour.
Sketch a graph that displays the cost against time.
Form an equation relating x and y.
Find the total cost for the business to operate for 22 hours.
Find the number of hours that the business needs to operate to incur a total cost of \$5400.
A baseball is thrown vertically upward, and the velocity of the baseball, V in metres per second after T seconds is given by V = 120 - 32 T.
Complete the following table of values:
| \text{Time } (T) | 0 | 1 | 2 | 3 | 4 |
|---|---|---|---|---|---|
| \text{ Velocity } (V) |
Graph the linear relationship represented in the table.
What does the negative value of V, when T = 4, mean in context?
Discuss the usefulness and limitations of this model.
A racing car starts the race with 250 litres of fuel. From there, it uses fuel at a rate of 5 litres per minute.
Complete the table of values:
| \text{Number of minutes passed, }x | 0 | 5 | 10 | 15 | 20 | 50 |
|---|---|---|---|---|---|---|
| \text{Amount of fuel left in tank, }y |
Determine an algebraic rule linking the number of minutes passed, x, and the amount of fuel left in the tank, y.
Describe how the amount of fuel in the car is changing over time.
Discuss the usefulness and limitations of this model.
The cost, y, for a business to operate, can be expressed in terms of x, the total number of hours it has operated for. The cost is \$120 an hour.
Sketch a graph that displays the cost against time.
State the gradient of the line.
Form an equation relating x and y.
Find the total cost for the business to operate for 28 hours.
Find the number of hours that the business needs to operate to incur a total cost of \$3840.
The table shows Peter's earnings from ironing shirts:
| Shirts sewed | 0 | 2 | 4 | 6 | 8 |
|---|---|---|---|---|---|
| Earnings | 4 | 8 | 12 | 16 | 20 |
Sketch the graph that depicts his earnings in dollars (y) against the number of shirts he irons (x).
Calculate the gradient of the line.
What does the gradient represent in this context?
What is the y-intercept of the line?
What does the y-intercept represent in this context?
What will be his total earnings if he irons a total of 14 shirts?
How many shirts will he have to iron in order to earn \$28?
A ball is rolled down a hill. The table below shows the velocity, in \text{m}/\text{s} of the ball after a given number of seconds:
| \text{Time in seconds, }t | 0 | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|---|
| \text{Velocity, }V | 18 | 19.7 | 21.4 | 23.1 | 24.8 | 26.5 |
Determine the rule that connects the velocity, V, to the time in seconds, t.
Graph the line that represents the relationship between velocity and time.
Calculate the gradient of the line.
Explain the meaning of the gradient of the line in this context.
Calculate the vertical intercept of the line.
Explain the meaning of the vertical intercept of the line in this context.
Find the velocity of the ball after 17 seconds, rounded to one decimal place.
Discuss the usefulness and limitations of this model.
The number of fish in a river is approximated over a five year period. The results are shown in the table below:
| \text{Time in years }(t) | 0 | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|---|
| \text{Number of fish }(F) | 6000 | 5700 | 5400 | 5100 | 4800 | 4500 |
Sketch the graph of the relationship on a number plane.
Calculate the gradient of the line.
What does the gradient represent in this context?
State the value of F when the line crosses the vertical axis.
Write an algebraic equation for the line relating t and F.
Hence determine the number of fish remaining in the river after 9 years.
Determine the number of years it takes for there to be 1800 fish remaining in the river.
Valentina left for a road trip at midday. The graph shows the total distance travelled (in kilometres) t hours after midday.
Let the horizontal axis represent the time in hours and the vertical axis represent the distance travelled in kilometers.
State the gradient of the line.
Explain the meaning of the gradient in this context.
The graph shows the temperature of a room after the heater has been turned on:
State the gradient of the line.
State the y-intercept.
Write an equation to represent the temperature of the room, y, as a function of time, t.
Explain the meaning of the gradient in this context.
Explain the meaning of the y-intercept in this context.
Find the temperature of the room after the heater has been turned on for 30 minutes.
Discuss the usefulness and limitations of this model.
The graph shows the amount of water remaining in a bucket that was initially full before a hole was made in it's side.
State the gradient of the line.
Find the y-intercept.
Write an equation to represent the amount of water remaining in the bucket, y, as a function of time, x.
Explain the meaning of the gradient in this context.
What does the y-intercept represent in this context?
Find the amount of water remaining in the bucket after 54 minutes.
The table shows the linear relationship between the number of plastic chairs manufactured, x, and the total manufacturing cost, y:
| Number of plastic chairs | 5 | 10 | 15 |
|---|---|---|---|
| Cost (dollars) | 135 | 185 | 235 |
State the gradient of the line.
Form an equation relating x and y.
Find the y-intercept.
Explain the meaning of the y-intercept in this context.
Explain the meaning of the gradient of the function in this context.
Find the total cost of manufacturing 25 plastic chairs.
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.
Discuss the usefulness and limitations of this model.
The graph shows the conversion between miles and kilometres:
Convert 10 miles to kilometres.
Hence, how many kilometres is 1 mile equal to?
The graph shows the conversion between temperatures in Celsius and Fahrenheit:
Use the graph to convert the following as indicated:
40 \degree\text{C} to Fahrenheit.
50 \degree\text{F} to Celsius.
- 20 \degree\text{F} to Celsius.
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? Normal body temperature is 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.
The graph shows the conversion between miles and kilometres:
If a car is driving 32 \text{ km/hr} in a school zone, at what speed are they travelling in miles per hour?
A road sign states the speed limit to be 128\text{ km/hr}. Calculate this speed limit in miles per hour.