#### Answer

slope is undefined;
the line is vertical

#### Work Step by Step

RECALL:
(i) The slope, $m$, of the line that passes through the points $(x_1, y_1)$ and $(x_2, y_2)$ is given by the formula:
$m=\dfrac{y_2-y_1}{x_2-x_1}$
(ii) A line whose slope is positive rises from left to right.
(iii) A line whose slope is negative falls from left to right.
(iv) A horizontal line has a slope of zero.
(v) A vertical line has an undefined slope.
Use the formula in (i) above to find the slope of the line that passes through the points $(a, b)$ and $(a, b+c)$ to obtain:
$m=\dfrac{(b+c) -b }{a-a}=\dfrac{c}{0}$ (slope is undefined)
The slope is undefined, so the line is vertical.