Linear Relations

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.

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

Number of litres ($x$x) |
$0$0 | $10$10 | $20$20 | $30$30 | $40$40 |
---|---|---|---|---|---|

Cost of gas ($y$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 gas pumped ($x$**`x`) and the cost of the gas ($y$`y`).**How much does gas cost per litre?****How much would $47$47 litres of gas cost at this unit price?****In the equation, $y=1.64x$**`y`=1.64`x`, 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**

**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`=50`n`$n$ `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`=25`n`+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.****Loading Graph...****A****Loading Graph...****B****Loading Graph...****C****Loading Graph...****D****Loading Graph...****A****Loading Graph...****B****Loading Graph...****C****Loading Graph...****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.**

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

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

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