5.2 Inverse Variation

5.2 Inverse Variation
If a quantity yvaries inversely as another quantity x, then
(a) y increases when x decreases,
(b) y decreases when x increases


5.2b Expressing an inverse variation in the form of an equation
An inverse variation can be written in the form of an equation, y = k x where k is a constant which can be determined.
 
Example 1:
Given y varies inversely as x and y = 4 when x =10. Write an equation which relates x and y.

Solution:
y 1 x y = k x 4 = k 10 k = 40 y = 40 x


Example 2:
Given that y = 3 when x = 6, find the equation relates x and y if:
( a ) y 1 x 2 (b) y 1 x 3 (c) y 1 x

Solution:
( a ) y 1 x 2 y = k x 2 3 = k 6 2 k = 3 × 36 = 108 y = 108 x 2 (b) y 1 x 3 y = k x 3 3 = k 6 3 k = 3 × 216 = 648 y = 648 x 3 (c) y 1 x y = k x 3 = k 6 k = 3 × 6 = 3 6 y = 3 6 x

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