Q22. - Algebra 2

Question

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

$(5,7),(4,-6)$

Step-by-Step Solution

Answer

The Slope of the line that passes through the points $(5,7),(4,-6)$ is 13.

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 $\left(5,7\right)\text{ and }(4,-6)$. Therefore, $x_1=5;x_2=4;y_1=7;y_2=-6$.

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

$\begin{array}{c}m=\frac{-6-7}{4-5}\\ =\frac{-13}{-1}\\ =13\end{array}$