#### Answer

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.

#### Work Step by Step

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.