Q27. - Algebra 2

Question

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

 $\left(5.5,-5.5\right),\left(11,-7\right)$

Step-by-Step Solution

Answer

The slope of the line is $m=\frac{-3}{11}$.

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 $\left(5.5,-5.5\right)\text{ and }\left(11,-7\right)$.

Here $\left(x_1,y_1\right)=\left(5.5,-5.5\right)\text{ and }\left(x_2,y_2\right)=\left(11,-7\right)$.

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

$\begin{array}{c}m=\frac{y_2-y_1}{x_2-x_1}\\ =\frac{-7-\left(-5.5\right)}{11-5.5}\end{array}$

Step-3 – Calculation

Simplify the value obtained for the slope of the line.

$\begin{array}{c}m=\frac{-7+5.5}{11-5.5}\\ =\frac{-1.5}{5.5}\\ =-\frac{15}{55}\\ =-\frac{3}{11}\end{array}$

Hence, the slope of the line passing through the points $\left(5.5,-5.5\right)\text{ and }\left(11,-7\right)$ is $m=\frac{-3}{11}$.