#### Answer

Slope is undefined, and the line is vertical.

#### Work Step by Step

The slope of the line through the points $(x_{1},y_{1})$ and $(x_{2},y_{2})$ is $m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$.
$m=\frac{\frac{1}{6}-(-6)}{\frac{3}{2}-\frac{3}{2}}$
$=\frac{\frac{37}{6}}{0}$
Since the denominator is a zero, slope is undefined, and the line is vertical.