Answer
Constant of Variation $= 6$
Work Step by Step
Recall:
An inverse variation is represented by the equation $xy=k$, where $k$ is the constant of variation.
As the value of $x$ increases, the value of $y$ decreases.
The equation that models the inverse variation can be determined by finding the value of $k$:
This can be done by taking any ordered pair $(x, y)$ then substituting the values of $x$ and $y$ into the inverse variation formula $xy=k$.
Since the variation contains the point $\left(\sqrt2, \sqrt{18}\right)$, substitute these into the formula $xy=k$ to obtain:
\begin{align*}
xy&=k\\\\
\sqrt2 \cdot \sqrt{18}&=k\\\\
\sqrt{2(18)}&=k\\\\
\sqrt{36}&=k\\\\
6&=k
\end{align*}
