Many years ago a teacher’s salary was based on the number of students he had. Suppose a salary of $60 per month was to be paid for 50 students and $50 a month for 30 students. If the actual enrollment was 45 students, what should the teacher be paid?

Let’s assume the salary formula, *f*, is a linear function and use the points (50, 60) and (30, 50) to find the equation for *f*:

We have *f* = [(60-50)/(50-30]*n* + *b* = .5*n* + *b*.

Then we substitute (30, 50) to solve for *b*: 50 = .5(30) + *b* → *b* = 35.

So *f* = .5*n* + 35.

Substituting *n* = 45, *f* = .5(45) + 35 = 22.50 + 35 = 57.50.

The teacher should be paid $57.50 per month for 45 students.