Ontario 09 Applied (MFM1P)
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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 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.  

Question 1

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

  2. How much does gas cost per litre?

  3. How much would $47$47 litres of gas 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 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

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

    Loading Graph...

    A

    Loading Graph...

    B

    Loading Graph...

    C

    Loading Graph...

    D

    Loading Graph...

    A

    Loading Graph...

    B

    Loading Graph...

    C

    Loading Graph...

    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.

 

 

 

 

 

Outcomes

9P.LR3.05

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

9P.LR4.01

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

9P.LR4.03

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

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