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Question

Part 1
State the independent variable and the dependent variable in the linear relationship. Then find the rate of change for the situation.
The cost of tickets is ​$65 for five teens and ​$91 for seven teens.
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Part 1
Determine the independent variable.
A.
the number of teens
B.seven teens
seven teens
C.five teens
five teens
D.
​$65
E.
​$91
F.
the cost of tickets

Answer 1

In this situation, the independent variable is the one that you can control or change, while the dependent variable changes based on the value of the independent variable.

Independent Variable: A. the number of teens

The cost of tickets depends on the number of teens, so the number of teens is your independent variable.

Dependent Variable: The dependent variable in this case would be the cost of tickets, which changes based on the number of teens.

Rate of Change: To find the rate of change, you can calculate the difference in costs divided by the difference in the number of teens.

1. Cost for five teens = $65
2. Cost for seven teens = $91
3. Difference in cost = $91 - $65 = $26
4. Difference in the number of teens = 7 - 5 = 2

Now, calculate the rate of change: \[ \text{Rate of Change} = \frac{\text{Difference in Cost}}{\text{Difference in Number of Teens}} = \frac{26}{2} = 13 \]

The rate of change is $13 per teen.