1. **State the problem:** We are given a table of values for $x$ and $y$ and need to find the rule (function) that relates $x$ to $y$. 2. **Given values:** $$\begin{array}{c|cccc} x & 1 & 2 & 3 & 4 \\ y & 100 & 50 & 33.3\overline{3} & 25 \\\end{array}$$ 3. **Look for a pattern:** Notice that as $x$ increases, $y$ decreases. The values suggest $y$ might be inversely proportional to $x$. 4. **Assume the function form:** $$y = \frac{k}{x}$$ where $k$ is a constant to be determined. 5. **Find $k$ using a known point:** Using $x=1$, $y=100$: $$100 = \frac{k}{1} \implies k = 100$$ 6. **Write the function rule:** $$y = \frac{100}{x}$$ 7. **Verify with other points:** - For $x=2$, $y = \frac{100}{2} = 50$ (matches table) - For $x=3$, $y = \frac{100}{3} = 33.3\overline{3}$ (matches table) - For $x=4$, $y = \frac{100}{4} = 25$ (matches table) **Final answer:** $$\boxed{y = \frac{100}{x}}$$