Answer
constant of variation $= k = 2$
inverse variation equation: $xy=2$
Work Step by Step
RECALL:
When $y$ varies inversely as $x$, the variation is represented by the equation $xy=k$ where $k$ is the constant of variation.
The given inverse variation has $y=3$ when $x=\frac{2}{3}$.
Substitute these values into x and y in the given equation above to obtain:
$xy=k
\\\frac{2}{3} \cdot 3 = k
\\2 = k$
Thus, the constant of variation is $2$ and the inverse variation is represented by the equation $xy=2$.
