Chapter 8.6, Problem 81S

To determine

To find:The slope of the line that passes through each pair of points.

Answer to Problem 81S

The slope for the pair of points $(2,-1)$ and $(5,-3)$ is

Explanation of Solution

Given information:

The pair of points $(2,-1)$ and $(5,-3)$ .

Calculation:

Consider the pair of points $(2,-1)$ and $(5,-3)$ .

The objective is to find the slope of the line that passes through the points $(2,-1)$ and $(5,-3)$ .

The slope of line passing from two points $\left(x_1,y_1\right)$ and $\left(x_2,y_2\right)$ is given as,

  $m=\frac{y_2-y_1}{x_2-x_1}$

Calculate the slope at point $(2,-1)$ and $(5,-3)$ as follows:

  $\begin{array}{cc}m==\frac{y_2-y_1}{x_2-x_1}& \\ & =\frac{-3-(-1)}{5-2}(2,-1)=\left(x_1,y_1\right)\text{and}(5,-3)=\left(x_2,y_2\right)\end{array}$

  $=\frac{-2}{3}$ Simplify

Hence, the slope for the pair of points $(2,-1)$ and $(5,-3)$ is