Question

What is the slope of a line that is perpendicular to the line represented by the equation x – y = 8? 1 −1 8

Answer 1

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

`x-y=8\implies -y=-x+8\implies y=\stackrel{\stackrel{m}{\downarrow }}{1}x-8\impliedby \begin{array} \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}{ 1 \implies \cfrac{1}{\underline{1}}} ~\hfill \stackrel{reciprocal}{\cfrac{\underline{1}}{1}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{\underline{1}}{1} \implies \text{\LARGE -1}}}`