Question

What is the average rate of change of g(x)=−6+5xg(x)=−6+5x between the points (−2,−16)(−2,−16) and (4,14)(4,14)?

Answer 1

By definition, the slope of the line is defined as:
m = (y2-y1) / (x2-x1)
Substituting the values
m = ((14) - (- 16)) / ((4) - (- 2)) = 5
Note that 5 is the same value as the slope of the line in function
g (x) = - 6 + 5x
The slope of the line will always be constant for any pair of points.
answer
the average rate of change is 5