# How do you write a general formula to describe each variation if y varies inversely with sqrt x; y =4 when x=9?

Feb 11, 2017

$\textcolor{b l u e}{y = \frac{12}{\sqrt{x}}}$

#### Explanation:

In an inverse variation, as one quantity increases, the other decreases: It is shown as $y \propto \frac{1}{x}$

However, in this case the inverse variation is with $\sqrt{x}$

$y \propto \frac{1}{\sqrt{x}}$

All variations (also called proportions) are connected by a constant,$k$

:. color(blue)(y = k/sqrtx)" larr we need to find the value of $k$

$k = y \times \sqrt{x} \text{ } \leftarrow$ isolate $k$ by cross- multiplying

Use the given values for $x \mathmr{and} y$

$k = 4 \times \sqrt{9} = 4 \times 3 = 12 \text{ }$ we now know $k$

Replace $k$ by $12$

$\therefore \textcolor{b l u e}{y = \frac{12}{\sqrt{x}}}$