1. **State the problem:** Given that $x$ varies inversely as $y$, and $x=4$ when $y=8$, find $x$ when $y=1$. 2. **Formula and rule:** For inverse variation, the relationship is given by $$x \times y = k$$ where $k$ is a constant. 3. **Find the constant $k$ using the given values:** $$4 \times 8 = k$$ $$k = 32$$ 4. **Use the constant $k$ to find $x$ when $y=1$:** $$x \times 1 = 32$$ $$x = 32$$ 5. **Final answer:** When $y=1$, $x=32$.