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Direct Proportion

Direct Proportion. Lesson Aims. To understand what is meant by direct proportion. Keywords. Proportionality Direct proportion Constant of proportionality. An Example of Direct Proportion. If I were to go shopping in Poundland and buy 5 items, the cost would be £5.

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Direct Proportion

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  1. Direct Proportion

  2. Lesson Aims • To understand what is meant by direct proportion.

  3. Keywords • Proportionality • Direct proportion • Constant of proportionality

  4. An Example of Direct Proportion • If I were to go shopping in Poundland and buy 5 items, the cost would be £5. • How much would it cost for 10 items? • £10 …. and so on

  5. So what can we say about the relationship between the price & number of items bought? • The more items that are bought the more it costs. (No.of items bought = price paid). • Therefore, the price and number of items are said to be directly proportional.

  6. Upmarket shopping! • This time we go shopping in Costalotmore where each item is £5. • Is this relationship directly proportional? How can we find out?

  7. Look at Ratios • We can look at the number of items and the cost of them in terms of their ratios. • 1:5, 2:10, 3:15 & 4:20. • What is the simplest form of each ratio? • 1:5 • As the price increases at the same rate as the number of items, they are directly proportional.

  8. Look at a graph

  9. Look at a graph Poundland y=x

  10. Look at a graph Costalotmore Poundland y=5x y=x

  11. Notation α (alpha) • αmeans proportional to or varies directly with. • y α x means that y is directly proportional to, or varies with x.

  12. Using the Notation • In the first graph example y=x, this can be written as: y α x

  13. In the second example y=5x can also be written as: y αx Why?

  14. General Equation The general equation for direct proportion is: y=kx where k is a constant amount and called the constant of proportion.

  15. Example If y α x and y=2 when x=3, find the equation connecting y to x.

  16. Solution using y = kx 1. Substitute values for x & y 2 = k x3 2. Re-arrange k = 2 3 3. Put it all back: y = 2 x 3

  17. Summary • When 2 quantities are in direct proportion, as one quantity increases the other quantity increases at the same rate. • y α xcan be expressed as: y = kx

  18. Non linear • The examples so far have been linear, ie of the form: y=kx • For non linear proportion, the general form becomes: y=kxn or y α kxn

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