Final answer:
In the given linear relationship, the independent variable is the number of people and the dependent variable is the cost of admission. The rate of change is found to be $13 per person.
Step-by-step explanation:
The question involves identifying the independent variable and the dependent variable in a linear relationship, as well as calculating the rate of change. When we talk about the cost of admission based on the number of people, the independent variable is the number of people, since it is the variable we change to see how it affects the cost. Conversely, the cost of admission is the dependent variable because it depends on the number of people.
To find the rate of change, we can use the given values: $39 for three people and $91 for seven people. The rate of change, also known as the slope in a linear equation, is found by calculating the change in cost divided by the change in the number of people:
Rate of change (slope) = (Cost for seven people - Cost for three people) / (Number of people in the second situation - Number of people in the first situation)
Rate of change (slope) = ($91 - $39) / (7 - 3) = $52 / 4 = $13 per person.
The rate of change is $13 per person, meaning for every additional person, the cost increases by $13.