Q12. - Algebra 1

Question

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

$\left(-4,7\right), \left(8,-1\right)$

Step-by-Step Solution

Answer

The slope of the line that passes through the given pair of points is $\frac{-2}{3}$.

Step 1. Write the formula to find the slope of the line that passes through two points.

The slope of the line (m) that passes through the two points $\left(x_1,y_1\right)$ and $\left(x_2,y_2\right)$ is:

width="87" style="max-width: none; vertical-align: -21px;" $m=\frac{y_2-y_1}{x_2-x_1}$

Step 2. Find the slope of the line that passes through the points − 4 , 7 and 8 , − 1 .

The slope of the line (m) that passes through the points $\left(x_1,y_1\right)=\left(-4,7\right)$ and $\left(x_2,y_2\right)=\left(8,-1\right)$ is:

 $$\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ =\frac{-1-7}{8-\left(-4\right)} \\ =\frac{-8}{8+4} \\ =\frac{-8}{12} \\ =\frac{-2}{3} \end{gathered}$$

 

The slope of the line that passes through the given pair of points is $\frac{-2}{3}$.