1. **State the problem:** We have a 17.5 inch candle that burns down completely in 10 hours. We want to write a proportional equation for $y$, the amount of candle burned in inches, in terms of $x$, the time in hours. 2. **Understand the relationship:** Since the candle burns down uniformly, the amount burned $y$ is directly proportional to the time $x$. This means we can write: $$y = kx$$ where $k$ is the constant of proportionality (rate of burning in inches per hour). 3. **Find the constant $k$:** The candle burns 17.5 inches in 10 hours, so: $$17.5 = k \times 10$$ 4. **Solve for $k$:** $$k = \frac{17.5}{10} = 1.75$$ 5. **Write the equation:** $$y = 1.75x$$ 6. **Interpretation:** This means the candle burns 1.75 inches every hour. **Final answer:** $$y = 1.75x$$