1. **State the problem:** We are given a graph showing a linear relationship between Time (seconds) and Distance (inches) with points (0,0), (1,1.5), and (3,4.5). We need to determine if $x$ (Time) and $y$ (Distance) are proportional. 2. **Recall the definition of proportionality:** Two variables $x$ and $y$ are proportional if there exists a constant $k$ such that $$y = kx$$ for all points. This means the ratio $\frac{y}{x}$ must be constant. 3. **Calculate the ratio $\frac{y}{x}$ for the given points:** - For $(1, 1.5)$: $$\frac{y}{x} = \frac{1.5}{1} = 1.5$$ - For $(3, 4.5)$: $$\frac{y}{x} = \frac{4.5}{3} = 1.5$$ 4. **Check the ratio at the origin:** At $(0,0)$, the ratio is undefined but this is acceptable since proportionality requires the line to pass through the origin. 5. **Conclusion:** Since the ratio $\frac{y}{x}$ is constant (1.5) for all nonzero $x$, $y$ and $x$ are proportional. **Final answer:** Yes, $x$ and $y$ are proportional because the graph is a straight line through the origin with a constant ratio $\frac{y}{x} = 1.5$.