Chapter 9.3, Problem 35STP

To determine

To choose : the correct answer concerning the slope of the line.

Answer to Problem 35STP

Option C. is the correct answer.

Explanation of Solution

Given information :

The line passes through the points $(-3,5)$ and $(6,-1)$ .

The given options:

A. $\frac{2}{5}$

B. $\frac{2}{3}$

C. $-\frac{2}{3}$

D. $-\frac{3}{2}$

Formula used:

The slope of a line:

  $m=\frac{y_2-y_1}{x_2-x_1}$ , where $x_2\ne x_1$

Calculation :

As per problem,

The line passes through the points $(-3,5)$ and $(6,-1)$

Take $y_1=5,y_2=-1,x_1=-3,\text{ and }{x}_2=6$

So, the slope of the line:

  $\begin{array}{l}m=\frac{y_2-y_1}{x_2-x_1}\text{ [Write the formula]}\\ m=\frac{-1-5}{6-(-3)}\text{ [}{y}_1=5,y_2=-1,x_1=-3,x_2=6]\\ m=\frac{-6}{9}=-\frac{2}{3}\text{ [Simplify]}\end{array}$

Therefore, the slope of the line is $-\frac{2}{3}$ .