Q26. - Algebra 2

Question

Find the slope of the line that passes through each pair of points. 

 $26.\left(-6,-3\right),\left(6,7\right)$

Step-by-Step Solution

Answer

The slope of the line is $m=\frac{5}{6}$.

Step-1 – Apply the concept of slope

The slope of the line passing through the points $\left(x_1,y_1\right)\text{ and }\left(x_2,y_2\right)$ is expressed below.

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

Step-2 –Substitute and solve

Consider the provided ordered pairs $\left(-6,-3\right)\text{ and }\left(6,7\right)$.

Here $\left(x_1,y_1\right)\text{=}\left(-6,-3\right)\text{ and }\left(x_2,y_2\right)=\left(6,7\right)$.

Recall the formula of slope of the line and apply it.

$\begin{array}{c}m=\frac{y_2-y_1}{x_2-x_1}\\ =\frac{7-\left(-3\right)}{6-\left(-6\right)}\end{array}$

Step-3 – Calculation

Simplify the value obtained for the slope of the line.

$\begin{array}{c}m=\frac{7+3}{6+6}\\ =\frac{10}{12}\\ =\frac{5}{6}\end{array}$

Hence, the slope of the line passing through the points $\left(-6,-3\right)\text{ and }\left(6,7\right)$ is $m=\frac{5}{6}$.