Chapter 4 - Exponential Functions - 4.1 Introduction to the Family of Exponential Functions - Exercises and Problems for Section 4.1 - Exercises and Problems - Page 148: 62

$m= b^5-b$

First find the coordinates of the two points on the graph. \begin{equation} \begin{aligned} P(x_1, y_1)&=(1, 4b)\\ Q(x_2, y_2)&=(5, 4b^5)\\ m&= \frac{y_2-y_1}{x_2-x_1}\\ &= \frac{4b^5-4b}{5-1}\\ &= b^5-b\\ y&= mx-mx_1+y_1\\ &= (b^5-b)x-(b^5-b)+4b\\ y&= (b^5-b)x-b^5+5b\\ \end{aligned} \end{equation} The slope of the line segment is $m= b^5-b$.