Question

Find the slope of a line perpendicular to the line whose equation is 4x−2y=20. Fully simplify your answer.

Answer 1

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

`4x-2y=20\implies -2y=-4x+20\implies y=\cfrac{-4x+20}{-2} \\\\\\ y=\stackrel{\stackrel{m}{\downarrow }}{2}x-10\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}{ 2 \implies \cfrac{2}{1}} ~\hfill \stackrel{reciprocal}{\cfrac{1}{2}} ~\hfill \stackrel{negative~reciprocal}{ {\Large \begin{array}{llll} -\cfrac{1}{2} \end{array}} }}`