Inverse Variation

For inverse variation, an increase in one quantity results in a decrease in the other and vice versa. 

For example: if one quantity is doubled, the other is halved. Thus if y varies inversely to x then we can write. 

\(\scriptsize y \propto \normalsize \frac{1}{x} \)

y = \( \frac{k}{x} \)

where k = constant

or y = \( \scriptsize k \: \times \: \normalsize \frac{1}{x} \)

Example 8.3.1:

y varies inversely as x, and y = 15 when x = 7.5 

(a) Find the equation connecting y and x
(b) Find the value of x when y = 10. 

Solution

a.

\(\scriptsize y \propto \normalsize \frac{1}{x} \)

y = \( \frac{k}{x} \)

where k = constant

multiply both sides by x to eliminate the fraction