Question

What is the average rate of change of `g(x)=2x-3` between the points (-2,-7) and (3,3)?

Answer 1

It is the same as the slope of the line through those points.

Explanation:

Using the definition
`(Delta y)/(Delta x) = (y_2-y_1)/(x_2-x_1) = (3-(-7))/(3-(-2)) = 10/5 = 2`

Using prior knowledge

The two points line on a line that has slope `2` so the slope of the line through the two points is `2`