Undefined Slope Definition
Undefined slope occurs when the slope is for a vertical line. A vertical line has an undefined slope because all points on the line have the same x-coordinate. As a result the formula m = Δy⁄Δx = y2 - y1⁄x2 - x1 used for slope results in a denominator of 0, which therefore makes the slope undefined.
“Undefined Slope.” Mathwords, www.mathwords.com/u/undefined_slope.htm.