Linear Relations

Lesson

It's great to understand linear relationships because if we can identify these kinds of relationships in everyday situations, we can solve all kinds of problems!

For example, what if we wanted to compare the cost of mobile plans between two companies? We definitely want to know which plan will cost the least so we can get the best deal.

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

a) Write an equation for the total cost $T$`T` of Kerry's current internet service over a period of $n$`n` months.

b) 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.

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

d) Fill in the table of values for the total cost of the fibre optic cable service, given by $T=25n+1200$`T`=25`n`+1200.

Express a linear relation as an equation in two variables, using the rate of change and the initial value

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