Question

Find the slope of the line containing the points (4,8) and (4,6) then find the slope of a line parallel to this line and the slope of the line perpendicular to this line.

Answer 1

To calculate the slope between 2 points we use the following equation:

$m=\frac{y_2-y_1}{x_2-x_1}$

Replacing the points:

$\begin{gathered} m=\frac{8-6}{4-4} \\ m=\frac{2}{0} \\ m\to\infty \end{gathered}$

In this case, when we find an infinite slope, it means that it is a line parallel to the Y axis. All parallel lines have the same slope.

For the perpendicular case, the slope is equal to:

$\begin{gathered} m_{\perp}=\frac{1}{m} \\ m_{\perp}=\frac{1}{\frac{2}{0}} \\ m_{\perp}=\frac{0}{2} \\ m_{\perp}=0 \end{gathered}$

For the perpendicular case, the slope is zero and would equal one parallel to the X axis.