Fill in the blanks
Suppose that the function f has the same average rate of change c between any two points.
(a) Find the average rate of change of f between the points a and x to show that
c = f(x) − f(a)/ x-a

The rate of change between any two points is

Rearrange the equation in part (a) to show that
f(x) = cx + (f(a) − ca)

Multiplying the equation in part(a) by x − a, we obtain f(x) − f(a) = c()

Rearranging and adding
f(a) to both sides, we have f(x) = cx + f(a) − (), as desired.

How does this show that f is a linear function? What is the slope, and what is the y-intercept?

Because this equation is of form f(x) = Ax + B with constants A= and
B = f(a) − it represents a linear function with slope of and y-intercept f(a) −