Q28. - Algebra 2

Question

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

$\left(-3,24\right),\left(10,-41\right)$

Step-by-Step Solution

Answer

The slope of the line is $m=-5$.

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 $\left(-3,24\right)\text{ and }\left(10,-41\right)$.

Here $\left(x_1,y_1\right)=\left(-3,24\right)\text{ and }\left(x_2,y_2\right)=\left(10,-41\right)$.

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

$\begin{array}{c}m=\frac{y_2-y_1}{x_2-x_1}\\ =\frac{-41-24}{10-\left(-3\right)}\end{array}$

Step-3 – Calculation

Simplify the value obtained for the slope of the line.

$\begin{array}{c}m=\frac{-41-24}{10+3}\\ =\frac{-65}{13}\\ =-5\end{array}$

Hence, the slope of the line passing through the points $\left(-3,24\right)\text{ and }\left(10,-41\right)$ is $m=-5$.