1. **State the problem:** We are given that quantities $x$ and $y$ are proportional, and we have pairs of values: $(9, 4.5)$, $(14, 7)$, and $(30, 15)$. We need to find the constant of proportionality $r$ in the equation $y = rx$. 2. **Formula and explanation:** When two quantities are proportional, their ratio is constant. This means: $$r = \frac{y}{x}$$ for all pairs $(x, y)$. 3. **Calculate $r$ using the given pairs:** - For $(9, 4.5)$: $$r = \frac{4.5}{9} = 0.5$$ - For $(14, 7)$: $$r = \frac{7}{14} = 0.5$$ - For $(30, 15)$: $$r = \frac{15}{30} = 0.5$$ 4. **Conclusion:** Since the ratio $\frac{y}{x}$ is the same for all pairs, the constant of proportionality is: $$r = 0.5$$ This means the equation relating $y$ and $x$ is: $$y = 0.5x$$