Question

1. entrance to a state park costs $6 per vehicle, plus $2 per person. the table shows the entry cost for several recent groups of visitors. is the relationship between the number of people and the total entrance cost a proportional relationship? circle one. yes no explain your thinking.

Explanation:

Step1: Recall the definition of proportionality

For two variables $x$ (number of people) and $y$ (total cost), a proportional relationship is of the form $y = kx$, where $k$ is a constant of proportionality.

Step2: Calculate the cost - per - person ratios

For the first row: $x_1 = 2$, $y_1=10$, the cost - per - person ratio is $\frac{y_1}{x_1}=\frac{10}{2}=5$.
For the second row: $x_2 = 3$, $y_2 = 12$, the cost - per - person ratio is $\frac{y_2}{x_2}=\frac{12}{3}=4$.
For the third row: $x_3 = 4$, $y_3 = 14$, the cost - per - person ratio is $\frac{y_3}{x_3}=\frac{14}{4}=3.5$.
For the fourth row: $x_4 = 10$, $y_4 = 26$, the cost - per - person ratio is $\frac{y_4}{x_4}=\frac{26}{10}=2.6$.
Since the cost - per - person ratios are not the same for all data points, the relationship is not proportional.

Answer:

No