Answer
slope of the line is undefined ; vertical
Work Step by Step
The slope of a line can be defined as the ratio of the vertical change to the horizontal change when moving from one fixed point to another along a line.
The general notation for the slope of a line is, $\left( m \right)$ is given by
$\text{m= }\frac{\text{change in vertical}}{\text{change in horizontal}}$
Let $\left( {{x}_{1}},{{y}_{1}} \right)$ represents point $\left( a,b \right)$ and $\left( {{x}_{2}},{{y}_{2}} \right)$ represents point $\left( a,b+c \right)$
Then,
$\begin{align}
& \text{m= }\frac{\text{change in vertical}}{\text{change in horizontal}} \\
& =\frac{{{y}_{2}}-{{y}_{1}}}{{{x}_{2}}-{{x}_{1}}} \\
& =\frac{\left( \left( b+c \right)-b \right)}{a-a} \\
& =\frac{c}{0}
\end{align}$
Hence, the slope of the line is undefined.
As slope of the line passing through the provided pair of points is not defined, therefore the line is vertical.
