Modelling Linear Relationships - graphs
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. 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$1.64 represent? The unit rate of cost of petrol per litre. The number of litres of petrol pumped. The total cost of petrol pumped.
Number of litres ($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
Question 2
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 Fill in the table of values for the total cost of the fibre optic cable service, given by $T=25n+1200$T=25n+1200 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. 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)
$\editable{}$
$\editable{}$
$\editable{}$
$\editable{}$
$\editable{}$
$n$n
$1$1
$6$6
$12$12
$18$18
$24$24
$T$T (dollars)
$\editable{}$
$\editable{}$
$\editable{}$
$\editable{}$
$\editable{}$