Question

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

$(-2,5),(4,5)$

Short answer

The Slope of the line that passes through the points $(-2,5),(4,5)$ is 0.

Step-by-step solution

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 $\left(-2,5\right)\text{and}\left(4,5\right)$. Therefore, $x_1=-2;x_2=4;y_1=5;y_2=5$.

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

$\begin{array}{c}m=\frac{5-5}{4-\left(-2\right)}\\ =\frac{0}{4+2}\\ =\frac{0}{6}\\ =0\end{array}$