Stage 4 - Stage 5

Modelling Linear Relationships - graphs

Lesson

Now that we know how

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.

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

Number of litres ($x$`x`)	$0$0	$10$10	$20$20	$30$30	$40$40
Cost of petrol ($y$`y`)	$0$0	$16.40$16.40	$32.80$32.80	$49.20$49.20	$65.60$65.60

Write an equation linking the number of litres of petrol pumped ($x$x) and the cost of the petrol ($y$y).
How much does petrol cost per litre?
How much would $47$47 litres of petrol cost at this unit price?
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

Kerry currently pays $\$50$$50 a month for her internet service. She is planning to switch to a fibre optic cable service.

Write an equation for the total cost $T$T of Kerry's current internet service over a period of $n$n months.
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.
Fill in the table of values for the total cost of the current internet service, given by $T=50n$T=50n

$n$n $1$1 $6$6 $12$12 $18$18 $24$24

$T$T ( $dollars$ ) $\editable{}$ $\editable{}$ $\editable{}$ $\editable{}$ $\editable{}$
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 $1$1 $6$6 $12$12 $18$18 $24$24

$T$T ( $dollars$ ) $\editable{}$ $\editable{}$ $\editable{}$ $\editable{}$ $\editable{}$
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.
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A
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B
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C
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D
Using the graph from the previous question, determine how many months it will take for Kerry to break even on her new internet service.

$n$`n`	$1$1	$6$6	$12$12	$18$18	$24$24
$T$`T` ( $dollars$ )	$\editable{}$	$\editable{}$	$\editable{}$	$\editable{}$	$\editable{}$