Answer
The slope is undefined and the line is vertical line.
Work Step by Step
Take \[\left( {{x}_{1}},{{y}_{1}} \right)=\left( a,b \right)\]and \[\left( {{x}_{2}},{{y}_{2}} \right)=\left( a,b+c \right)\].
Slope of the line is:
\[m=\frac{{{y}_{2}}-{{y}_{1}}}{{{x}_{2}}-{{x}_{1}}}\]
\[\begin{align}
& m=\frac{b+c-b}{a-a} \\
& =\frac{c}{0}
\end{align}\]
Therefore, the slope of the line is undefined.
The slope is undefined,so the line is vertical line.
