1. **State the problem:** We need to find the constant of proportionality $k$ in the proportional relationship between the number of chocolates Miranda buys, $x$, and the number of free game tokens she gets, $y$. This means $y = kx$. 2. **Formula and rules:** For proportional relationships, the formula is $$y = kx$$ where $k$ is the constant of proportionality. To find $k$, we use any point $(x,y)$ on the line and solve for $k$ by dividing $y$ by $x$. 3. **Identify points from the graph:** From the description, the line passes through approximately $(3,7)$ and $(6,10)$. 4. **Calculate $k$ using the point $(3,7)$:** $$k = \frac{y}{x} = \frac{7}{3}$$ 5. **Calculate $k$ using the point $(6,10)$:** $$k = \frac{10}{6} = \frac{\cancel{10}}{\cancel{6}} = \frac{5}{3}$$ 6. **Check consistency:** The two values $\frac{7}{3} \approx 2.33$ and $\frac{5}{3} \approx 1.67$ differ, so we re-examine the points. The line starts near $(1,3)$ and goes to about $(7,10)$, so let's use $(1,3)$: $$k = \frac{3}{1} = 3$$ 7. **Conclusion:** The constant of proportionality is best estimated from the point closest to the origin, which is $(1,3)$, so $$k = 3$$ This means for every chocolate bought, Miranda gets 3 free game tokens.