finding the constant of proportionality from a graph\nhealth club rates\nuse the graph to find the unit…

Explanation:

Step1: Recall unit - rate formula

The unit rate (constant of proportionality) $k$ in a proportional relationship $y = kx$ is given by $k=\frac{y}{x}$, where $y$ is the cost and $x$ is the number of family members.

Step2: Select a point on the graph

Let's take the point $(2,84)$ from the graph. Here, $x = 2$ (number of family members) and $y=84$ (monthly cost).

Step3: Calculate the unit rate

$k=\frac{y}{x}=\frac{84}{2}=42$.

Answer:

$42$ per person, so the answer is $$42$ per person.