# Modelling linear relationships - graphs

Lesson

Now that we know how

• to graph linear relationships
• to find the equations of linear functions
• to use algebra and graphs to extract information and
• the slope of a linear function represents constant change,

we can put this to use to solve a range of real life applications.

It's all the same mathematics, but this time you will have a context to put upon it.

Some examples will be the best way to show you how the mathematics we have learnt can be applied to everyday situations.

##### Question 1

Gas costs a certain amount per litre. The table shows the cost of various amounts of gas.

 Number of litres ($x$x) Cost of gas ($y$y) $0$0 $10$10 $20$20 $30$30 $40$40 $0$0 $16.40$16.40 $32.80$32.80 $49.20$49.20 $65.60$65.60
1. Write an equation linking the number of litres of gas pumped ($x$x) and the cost of the gas ($y$y).

2. How much does gas cost per litre?

3. How much would $47$47 litres of gas cost at this unit price?

4. In the equation, $y=1.64x$y=1.64x, what does $1.64$1.64 represent?

The unit rate of cost of gas per litre.

A

The number of litres of gas pumped.

B

The total cost of gas pumped.

C

The unit rate of cost of gas per litre.

A

The number of litres of gas pumped.

B

The total cost of gas pumped.

C

##### Question 2

Kerry currently pays $\$50$$50 a month for her internet service. She is planning to switch to a fibre optic cable service. 1. Write an equation for the total cost TT of Kerry's current internet service over a period of nn months. 2. For the fibre optic cable service, Kerry pays a one-off amount of \1200$$1200 for the installation costs and then a monthly fee of $\$2525. Write an equation of the total cost $T$T of Kerry's new internet service over $n$n months.

3. Fill in the table of values for the total cost of the current internet service, given by $T=50n$T=50n

 $n$n $T$T (dollars) $1$1 $6$6 $12$12 $18$18 $24$24 $\editable{}$ $\editable{}$ $\editable{}$ $\editable{}$ $\editable{}$
4. Fill in the table of values for the total cost of the fibre optic cable service, given by $T=25n+1200$T=25n+1200

 $n$n $T$T (dollars) $1$1 $6$6 $12$12 $18$18 $24$24 $\editable{}$ $\editable{}$ $\editable{}$ $\editable{}$ $\editable{}$
5. Choose the correct pair of lines that show the total cost of Kerry's current internet service and the total cost of her new internet service.

A

B

C

D

A

B

C

D
6. Using the graph from the previous question, determine how many months it will take for Kerry to break even on her new internet service.

### Outcomes

#### 9P.LR3.05

Describe the meaning of the rate of change and the initial value for a linear relation arising from a realistic situation and describe a situation that could be modelled by a given linear equation

#### 9P.LR4.01

Determine values of a linear relation by using a table of values, by using the equation of the relation, and by interpolating or extrapolating from the graph of the relation

#### 9P.LR4.03

Determine other representations of a linear relation arising from a realistic situation, given one representation