Question

What is the slope of a line perpendicular to y=-1/2x-6?

Answer 1

Answer: 2

Explanation: Find the negative reciprocal of the slope of the original line.

Answer 2

keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the equation above

`y=\stackrel{\stackrel{m}{\downarrow }}{-\cfrac{1}{2}}x-6\qquad \impliedby \qquad \begin{array}ll \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array} \\\\[-0.35em] ~\dotfill`

`\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{ \cfrac{-1}{2}} ~\hfill \stackrel{reciprocal}{\cfrac{2}{-1}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{2}{-1} \implies \text{\LARGE 2}}}`