1. The problem states that $x$ and $y$ vary inversely, meaning their product is constant. This can be written as the formula: $$xy = k$$ where $k$ is a constant. 2. Using the given values $x=1$ and $y=9$, substitute into the formula to find $k$: $$1 \times 9 = k$$ $$k = 9$$ 3. Now the equation relating $x$ and $y$ is: $$xy = 9$$ or equivalently, $$y = \frac{9}{x}$$ 4. To find $y$ when $x=3$, substitute $3$ for $x$: $$y = \frac{9}{3}$$ 5. Simplify the fraction: $$y = \frac{\cancel{9}}{\cancel{3}} = 3$$ 6. Therefore, when $x=3$, $y=3$. Final answer: $y=3$ when $x=3$.