Q20. - Algebra 2

Question

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

$(8,-4),(6,1)$

Step-by-Step Solution

Answer

The Slope of the line that passes through the points $(8,-4),(6,1)$ is $-\frac{5}{2}$.

Step-1 – Apply the concept of slope

The slope of a line is the ratio of the change in the y-coordinates to the change in the x- coordinates.

Symbolically, the slope m of the line passing through the points $\left(x_1,y_1\right)\text{ and }\left(x_2,y_2\right)$ is given by $m=\frac{y_2-y_1}{x_2-x_1}$ where $x_1\ne x_2$.

Step-2 – Example of a slope through two points

Suppose a line passes through the points $(2,4),(3,0)$. Then the slope of the line passing through these points is given by 

$\begin{array}{c}m=\frac{0-4}{3-2}\\ =\frac{-4}{1}\\ =-4\end{array}$

Step-3 – Calculate the slope of the given points

The given points are $\left(8,-4\right)\text{ and }(6,1)$. Therefore, $x_1=8;x_2=6;y_1=-4;y_2=1$.

Hence the slope of the line through these points is calculated as 

$\begin{array}{c}m=\frac{1-\left(-4\right)}{6-8}\\ =\frac{1+4}{-2}\\ =\frac{5}{-2}\\ =-\frac{5}{2}\end{array}$