Answer
$y=\frac{2}{3} \sqrt{x}$
Work Step by Step
$y$ varies directly with $\sqrt{x}$ so the equation that represents the variation is of the form $y=k\sqrt{x}$ where $k$ is the constant of variation.
Given that $y=2$ when $x=9$, substituting these values into the equation above gives:
\begin{array}{l}
2=k \sqrt{9} \\
2=k \times 3 \\
k=\frac{2}{3}
\end{array}
Substitute $k=\frac{2}{3}$ in the equation to obtain $y=\frac{2}{3} \sqrt{x}$.
