Answer
$k=2$, $y=\frac{2}{x}$
Work Step by Step
If y varies inversely as x, we know that the variables x and y can be related by the function $y=\frac{k}{x}$, where k is the constant of proportionality.
If $y=\frac{1}{8}$ when $x=16$, then we know that $\frac{1}{8}=\frac{k}{16}$. Multiply both sides by 16.
$k=\frac{16}{8}=2$
Therefore, the constant of variation is $k=2$ and the inverse variation equation is $y=\frac{2}{x}$.
