#### Answer

variation constant $=k=9$
equation of the variation: $y=\frac{9}{x}$

#### Work Step by Step

$y$ varies inversely as $x$ so the variation is inverse.
The equation of an inverse variation is of the form $y=\frac{k}{x}$ where $k$ is the constant of variation.
To find the value of $k$ substitute the given values of $x$ and $y$ into $y=\frac{k}{x}$ to obtain:
$$y=\frac{k}{x}
\\81=\dfrac{k}{\frac{1}{9}}
\\81 = k \cdot \frac{9}{1}
\\81=9k
\\\frac{81}{9}=\frac{9k}{9}
\\9=k$$
Thus, the equation of the variation is $y=\frac{9}{x}$.