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| Algebraic Direct and Inverse Proportion |
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Direct Proportion (Algebraic)
If two variables y and x are in direct proportion, we can write down an equation connecting them.
Equation for direct proportion
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y = kx |
where k is a constant. |
Examples of problems
1) Given that y is directly proportional to x and that y = 56 when x = 8. Calculate y when x = 12.
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| a) Find the value of k: |
y = kx |
x = 8 |
y = 56 |
56 = k x 8
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k = 56/8
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k = 7
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| b) Substitute k = 7 into the equation: y = 7x. |
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‘when x = 12’ |
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y = 7 x 12
y = 84 |
2) Given that p is directly proportional to t2 and that p = 16 when t = 2.
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a) Calculate p when t = 5. |
b) Calculate t when p = 81.
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a) p = kt2 |
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16 = k x 4
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k = 4
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p = 4t2
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(t = 5)
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p = 4 x 25
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p = 100 |
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b) p = 4t2 |
(p = 81) |
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81 = 4 x t2
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t2 = 81/4
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t = 9/2
t = 4,5 |
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Inverse Proportion
| If two variables y and x are in inverse proportion, the equation is: |
y = k/x |
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Examples of problems
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1) If y is inversely proportional to x and y = 5 when x = 4,
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w and f = 10 when w = 16,
