Question

What is the slope of a line perpendicular to the line whose equation is x - 6y = 24.

Fully simplify your answer.

Answer 1

-6

Explanation:

i just got this question and it wasn’t 1/6 it was -6

Answer 2

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

`x-6y=24\implies -6y=-x+24\implies y=\cfrac{-x+24}{-6} \\\\\\ y=\cfrac{-x}{-6}+\cfrac{24}{-6}\implies y=\stackrel{\stackrel{m}{\downarrow }}{\cfrac{1}{6}} x-4\qquad \impliedby \begin{array}c \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}{6}} ~\hfill \stackrel{reciprocal}{\cfrac{6}{1}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{6}{1}\implies {\Large \begin{array}{llll} -6 \end{array}}}}`