1. **State the problem:** We know that $y$ is proportional to the square root of $x$, written as $y \propto \sqrt{x}$. Given $y=17$ when $x=25$, find $y$ when $x=14$, rounding to 1 decimal place. 2. **Write the formula:** Since $y$ is proportional to $\sqrt{x}$, we can write: $$y = k \sqrt{x}$$ where $k$ is the constant of proportionality. 3. **Find $k$ using the given values:** Substitute $y=17$ and $x=25$: $$17 = k \sqrt{25}$$ $$17 = k \times 5$$ $$k = \frac{17}{5} = 3.4$$ 4. **Find $y$ when $x=14$:** Substitute $k=3.4$ and $x=14$: $$y = 3.4 \sqrt{14}$$ Calculate $\sqrt{14} \approx 3.7417$: $$y \approx 3.4 \times 3.7417 = 12.722$$ 5. **Round to 1 decimal place:** $$y \approx 12.7$$ **Final answer:** $y = 12.7$ when $x=14$.