Question

For a school group, a skating rink charges a flat fee of $50 for skates for the students to use the skating rink.

•For 40 Students the skating rink charges 180.
•For 75 students, the skating rink charges 293.75
Which question represents the amount the skating rink charges for x students?
A)y=3.25x+35
B)y=3.25x+ 50
C)y=4.50x+ 35
D) y=4.50x+ 50

Answer 1

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:

`m= (293.75-180)/(75-40) = (113.75)/(35) \\ \\ m=3.25`

Linear function structure is:

`y=mx+b`
Where b is the y-intercept, which in this case is the fixed part, 50.
Finally, the function is:

`y=3.25x+50`

Attached picture shows its graph.