Question

What is the equation of the line that passes through the point (6,-2) and has an

undefined slope?

Answer 1

keeping in mind that a line with an undefined slope is always a vertical line, check the picture below.

now, we could use those two points from that line and check its slope

`(\stackrel{x_1}{6}~,~\stackrel{y_1}{-2})\qquad (\stackrel{x_2}{6}~,~\stackrel{y_2}{4}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{4}-\stackrel{y1}{(-2)}}}{\underset{run} {\underset{x_2}{6}-\underset{x_1}{6}}} \implies \cfrac{4 +2}{0}\implies \cfrac{6}{0}\implies und efined`