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Question
Find constant of variation and write equation of variation for the example given below.
x ∝ \[\frac{1}{\sqrt{y}}\] ; if x = 15 then y = 9
Solution
\[x \propto \frac{1}{\sqrt{y}}\]
\[\therefore x = \frac{k}{\sqrt{y}}\], where k is constant of variation
When x = 15, y = 9.
\[\therefore 15 = \frac{k}{\sqrt{9}}\]
\[ \Rightarrow 15 = \frac{k}{3}\]
\[ \Rightarrow k = 15 \times 3 = 45\]
So, the equation of variation is \[x = \frac{45}{\sqrt{y}}\] or \[x\sqrt{y} = 45\].
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