Chapter 13.2, Problem 13WE

To determine

To find the slope and length of the line $\overline{AB}$ .

Answer to Problem 13WE

The slope of line is $-0.4$ and length of the line $\overline{AB}$ is $2\sqrt{41}$ units.

Explanation of Solution

Given:

The coordinates of point $A,B$ are $\left(-3,-2\right)\text{ and }\left(7,-6\right)$

Calculation:

Slope of a line when two points $\left(x_1,y_1\right)$ and $\left(x_2,y_2\right)$ are given is

  $m=\frac{y_2-y_1}{x_2-x_1}$

Points given are $\left(-3,-2\right)\text{ and }\left(7,-6\right)$

  $m=\frac{-6-\left(-2\right)}{\left(7\right)-\left(-3\right)}=\frac{-4}{10}=-0.4$

Length of the line $\overline{AB}$ :

  $\sqrt{{\left(x_2-x_1\right)}^2+{\left(y_2-y_1\right)}^2}=\sqrt{{\left(7-\left(-3\right)\right)}^2+{\left(-6-\left(-2\right)\right)}^2}=2\sqrt{41}$

Therefore , the slope of line is $-0.4$ and length of the line $\overline{AB}$ is $2\sqrt{41}$ units.