Question

An athletic club has an application fee of $25 and a monthly membership fee of $15. The function f models the total cost of the membership if the application fee is waived. Write each function and compare the slopes and y-intercepts of the functions. Please explain

Answer 1

Answer:

The slopes are the same and produce parallel lines. The y-intercepts are different where one is 25 due to the $25 application fee and the other is 0 because the fee has been waived.

f(x)=15x

g(x)=15x+25

Step-by-step explanation:

Using slope-intercept form, f(x)=mx+b, we can substitute m=the constant rate of change being charged for x months and b the one time fee paid. This will give us f(x) or the total cost of membership.

With an application fee:

We substitute m=15 since our cost steadily rises each month by 15. This is our slope. But we must also add the one time application fee by substituting b=25. This becomes:

g(x)=15x+25.

Without an application fee:

We substitute m=15 since our cost steadily rises each month by 15. This is our slope. Since our application fee was waved, b=0.

f(x)=15x.

Comparing the two functions on a graph will show parallel lines that do not cross because they share the same m or slope. We would also see that they cross the y-axis at different points due to their different values for b.