QUESTION 11 Instructions: - Identify the independent and dependent variables for the given linear situation. - Write an equation that represents the linear relationship between the variables. - Use the equation to answer the question. Be prepared to show how you used the function equation to answer the question. Situation: There is a linear relationship between the total cost of a gym membership for the month and the number of fitness class taken that month. One month Mari took 12 classes and it cost her \( \$ 96 \). Another month she took 7 classes and paid \( \$ 56 \). Question: What is the total cost of a gym membership for the month if Mari attended 9 classes? Round final answer to the nearest cent if rounding is necessary. Answer: The total cost is \( \$ \)

To determine the independent and dependent variables, we can define the number of fitness classes taken in a month as the independent variable (let's call it \( x \)), and the total cost of the gym membership as the dependent variable (let's call it \( y \)). To find the equation representing the linear relationship, we first identify two points based on the data: (12, 96) and (7, 56). We can calculate the slope \( m \) using the formula \( m = \frac{y_2 - y_1}{x_2 - x_1} \): \[ m = \frac{56 - 96}{7 - 12} = \frac{-40}{-5} = 8 \] Now that we have the slope, we can use one of the points to find the slope-intercept form of the equation \( y = mx + b \). Using the point (12, 96): \[ 96 = 8(12) + b \implies 96 = 96 + b \implies b = 0 \] Thus, the equation is \[ y = 8x \] Now, to find the cost when Mari attended 9 classes: \[ y = 8(9) = 72 \] So, if Mari attended 9 classes, the total cost is \( \$72.00 \).