## Precalculus (6th Edition) Blitzer

The slope of the line passing through the points $\left( -2,5 \right)$ and $\left( -2,10 \right)$ is undefined and this line is vertical.
The slope of the line passing through two points $\left( {{x}_{1}},{{y}_{1}} \right)$ and $\left( {{x}_{2}},{{y}_{2}} \right)$ is provided by the formula $m=\frac{{{y}_{2}}-{{y}_{1}}}{{{x}_{2}}-{{x}_{1}}}$. Now, calculate the slope of the line passing through the points $\left( -2,5 \right)$ and $\left( -2,10 \right)$ is shown below: \begin{align} & m=\frac{10-5}{-2+2} \\ & =\frac{5}{0} \\ & =\infty \end{align} Therefore, the slope of this line is undefined. Since the slope of the line is undefined, thus the line is vertical; that is, it is parallel to the $y$ axis. Therefore, the slope of the line passing through the points $\left( -2,5 \right)$ and $\left( -2,10 \right)$ is undefined and this line is vertical.