Linear Equations
UK Secondary (7-11)
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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 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.

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

  2. How much does petrol cost per litre?

  3. How much would $47$47 litres of petrol 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 petrol per litre.

    A

    The number of litres of petrol pumped.

    B

    The total cost of petrol pumped.

    C

    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

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 (pounds) $\editable{}$ $\editable{}$ $\editable{}$ $\editable{}$ $\editable{}$
  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 (pounds) $\editable{}$ $\editable{}$ $\editable{}$ $\editable{}$ $\editable{}$
  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

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    B

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    C

    Loading Graph...

    D

    Loading Graph...

    A

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    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.

 

 

 

 

 

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