Question

What is the slope perpendicular to y=-3

Answer 1

check the picture below.

so, y = -3 is simply a horizontal line, as you see there, and any perpendicular line to that will be a vertical one, whose slope is undefined.

we can check by simply picking two points off the red line hmmm say (-2,2) and (-2, -2)

$\bf (\stackrel{x_1}{-2}~,~\stackrel{y_1}{2})\qquad (\stackrel{x_2}{-2}~,~\stackrel{y_2}{-2}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{-2-2}{-2-(-2)}\implies \cfrac{-2-2}{-2+2}\implies \stackrel{und efined}{\cfrac{-4}{0}}$