1. **State the problem:** Isaiah and his friends are sailing, and the distance from shore $y$ (in miles) is proportional to the time $x$ (in hours) they spend sailing. 2. **Understand proportional relationships:** If $y$ is proportional to $x$, then $y = kx$ where $k$ is the constant of proportionality. 3. **Use given points:** From the graph, the line passes through points $(1, 5)$ and $(5, 50)$. 4. **Calculate the constant of proportionality $k$:** Using the point $(1, 5)$: $$k = \frac{y}{x} = \frac{5}{1} = 5$$ Using the point $(5, 50)$: $$k = \frac{50}{5} = 10$$ Since these two values differ, check the problem carefully. The problem states a proportional relationship, so the points must satisfy $y = kx$ for the same $k$. 5. **Re-examine the points:** The problem states the line passes through $(1,5)$ and $(5,50)$, but these points do not lie on the same proportional line because $5 \times 5 = 25 \neq 50$. 6. **Check the graph description:** The line passes through $(1,5)$ and $(10,50)$ (not $(5,50)$) as per the graph description. 7. **Calculate $k$ using $(1,5)$ and $(10,50)$:** $$k = \frac{50}{10} = 5$$ 8. **Conclusion:** The constant of proportionality is $5$ miles per hour. **Final answer:** $$\boxed{5}$$ miles per hour