find the unit rate (constant of proportionality) for sam.\ndistance / time = 20 / 2 = 10 miles / hour…

Explanation:

Step1: Recall unit - rate formula

The unit rate (constant of proportionality) for a distance - time relationship is given by $\frac{\text{Distance}}{\text{Time}}$. For Bobby, if we assume the points are in the form $(t,d)$ where $t$ is time and $d$ is distance, and the relationship is proportional $d = kt$ (where $k$ is the constant of proportionality). Let's assume the points for Bobby are $(2, d_1)$ and $(4, d_2)$. Since the relationship is proportional, the constant of proportionality $k=\frac{d_1}{2}=\frac{d_2}{4}$. If we assume the points are on a straight - line passing through the origin (proportional relationship), we can use the fact that for a proportional relationship $y = kx$. Here, if $x$ is time and $y$ is distance, and we know that when $x = 2$ and $x = 4$, the ratio $\frac{y}{x}$ is constant. Let's say the distance for time $t = 2$ is $d_1$ and for $t = 4$ is $d_2$. Since $\frac{d_1}{2}=\frac{d_2}{4}=k$. If we assume the relationship is linear and proportional, we can take two points $(2,10)$ and $(4,20)$ (assuming a linear - proportional relationship where the rate is consistent). Then the unit rate (constant of proportionality) for Bobby is $\frac{\text{Distance}}{\text{Time}}$. Using the points $(2,10)$ and $(4,20)$:

Step2: Calculate the unit rate for Bobby

$k=\frac{10}{2}=\frac{20}{4}= 5$ miles per hour.

Answer:

The unit rate (constant of proportionality) for Bobby is 5 miles per hour.