Question

2 customers at the gym pay a membership fee to join and then a fee for each class they attend. here is a graph that represents the situation. part a what does the slope of the line shown by the points mean in this situation? enter your answer(s) here part b what does the vertical intercept mean in this situation? enter your answer(s) here

Explanation:

Part A

The slope of a line in a cost - number of classes relationship represents the rate of change of cost with respect to the number of classes. In the context of the gym membership, when we consider the linear relationship \(y = mx + b\) (where \(y\) is the total cost, \(x\) is the number of classes, \(m\) is the slope, and \(b\) is the \(y\) - intercept), the slope \(m=\frac{\Delta y}{\Delta x}\). Here, \(\Delta y\) is the change in cost and \(\Delta x\) is the change in the number of classes. So, the slope represents the cost per class.

Part B

The vertical intercept (or \(y\) - intercept) of a line \(y = mx + b\) occurs when \(x = 0\). In the context of the gym membership problem, when \(x = 0\) (i.e., the number of classes attended is \(0\)), the value of \(y\) (the total cost) is equal to the \(y\) - intercept. So, the vertical intercept represents the membership fee (the cost to join the gym before attending any classes).

Answer:

Part A

The slope means the cost per class.

Part B

The vertical intercept means the membership fee (the cost to join the gym).