 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 gradient 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

Petrol costs a certain amount per litre. The table shows the cost of various amounts of petrol.

 Number of litres ($x$x) Cost of petrol ($y$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$65.60
1. Write an equation linking the number of litres of petrol pumped ($x$x) and the cost of the petrol ($y$y).

2. How much does petrol cost per litre?

3. How much would $47$47 litres of petrol 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 petrol per litre.

A

The number of litres of petrol pumped.

B

The total cost of petrol pumped.

C

The unit rate of cost of petrol per litre.

A

The number of litres of petrol pumped.

B

The total cost of petrol 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 $T$T of Kerry's current internet service over a period of $n$n 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 $£25$£25. 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 (pounds) $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 (pounds) $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.