Chapter 8, Problem 29SGR

To determine

To find: The slope of the line

Answer to Problem 29SGR

The slope of line is -1.

Explanation of Solution

Given:

  $A\left(-3,7\right),G\left(5,-1\right)$

Formula used:

Slope of line is calculated by

  $m=\frac{y_2-y_1}{x_2-x_1}$

Calculation:

Consider two points: $A\left(-3,7\right)$ and $G\left(5,-1\right)$

Slope of the line (m) passing through two points is ratio of the difference in y-coordinates to the corresponding difference in x-coordinates.

So, if two points $\left(x_1,y_1\right)$ and $\left(x_2,y_2\right)$ then slope is:

  $m=\frac{y_2-y_1}{x_2-x_1}$

Consider that $\left(x_1,y_1\right)=\left(-3,7\right)$ and $\left(x_2,y_2\right)=\left(5,-1\right)$

Put the value in slope formula:

  $\begin{array}{l}m=\frac{-1-7}{5-\left(-3\right)}\\ =\frac{-8}{5+3}\\ =\frac{-8}{8}\\ =-1\end{array}$

Conclusion:

Therefore, the slope of line is -1.