Chapter 3.3, Problem 32PPS

To determine

The slope of the line that passes through the points $\left(8,10\right),\text{ and }\left(-4,-6\right)$ .

Answer to Problem 32PPS

  $\frac{4}{3}$

Explanation of Solution

Given information:

The pair of points, $\left(8,10\right),\text{ and }\left(-4,-6\right)$

Concept Used:

The slope of a line connecting the points $\left(x_1,y_1\right),\text{ and }\left(x_2,y_2\right)$ is given by the formula

  $\text{Slope }\left(m\right)=\frac{y_2-y_1}{x_2-x_1}$

Calculation:

In order to find the slope of the line passing through the points $\left(8,10\right),\text{ and }\left(-4,-6\right)$ , use the slope formula and substitute the values $\left(x_1,y_1\right)=\left(8,10\right),\text{ and }\left(x_2,y_2\right)=\left(-4,-6\right)$ and simplify further as shown below,

  $\begin{array}{c}\text{Slope }\left(m\right)=\frac{y_2-y_1}{x_2-x_1}\\ =\frac{-6-10}{-4-8}\\ =\frac{-16}{-12}\\ =\frac{16}{12}\\ =\frac{4}{3}\end{array}$

Thus, the slope of the line passing through the given points is $\frac{4}{3}$ .