Chapter SH, Problem 2.14EP

To determine

To find:the slope of the line passing through the given points.

Answer to Problem 2.14EP

  $m=\frac{1}{2}$ .

Explanation of Solution

Given:

The given points are $\left(-4,2\right),\left(2,5\right)$ .

Calculation:

The given points are $\left(-4,2\right),\left(2,5\right)$ .

From the given points,

  $\begin{array}{l}{x}_1=-4,y_1=2\\ x_2=2,y_2=5\end{array}$

As it is known that the slope of the line passing through the points is $m=\frac{y_2-y_1}{x_2-x_1}$ . Therefore,

  $\begin{array}{l}m=\frac{y_2-y_1}{x_2-x_1}\left\{\text{slope of the line}\right\}\\ m=\frac{5-2}{2-\left(-4\right)}\left\{\text{substitute these value}\right\}\\ m=\frac{3}{2+4}\left\{\text{simplify}\right\}\\ \therefore m=\frac{3}{6}\left\{\text{divide }6\text{ on each side}\right\}\\ \Rightarrow m=\frac{1}{2}\end{array}$

Hence, the slope of the line passing through the given points is $m=3$ .