5.2 Inverse Variation

5.2 Inverse Variation
If a quantity y varies 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