Question

write as a power function: y varies inversely with x and y is \\(\frac{2}{3}\\) when x is 9. \\(y = \frac{?}{\quad}\\)

Explanation:

Step1: Define inverse variation form

$y = \frac{k}{x}$ where $k$ is the constant of variation.

Step2: Substitute given values to find k

Substitute $y=\frac{2}{3}$, $x=9$:
$\frac{2}{3} = \frac{k}{9}$
Solve for $k$: $k = \frac{2}{3} \times 9 = 6$

Step3: Write final power function

Substitute $k=6$ back into the inverse variation form.

Answer:

$y = \frac{6}{x}$