The function has a variable part and a fixed part.
That fixed part is given by the fee for skates, which is $50.
The variable part depends on the quantity of students which is called 'x'. For this part, you are provided with a couple of points where the linear function passes by, they are: A(40,180) and B(75,293.75).
So, first thing to do is getting the slope:
[tex]m= \dfrac{293.75-180}{75-40} = \dfrac{113.75}{35} \\ \\ m=3.25[/tex]
Linear function structure is:
[tex]y=mx+b[/tex]
Where b is the y-intercept, which in this case is the fixed part, 50.
Finally, the function is:
[tex]y=3.25x+50[/tex]
Attached picture shows its graph.
