Question

Find the slope of the line that is perpendicular to the line 2x+6y=9

Answer 1

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

`2x+6y=9\implies 6y=-2x+9 \\\\\\ y=\cfrac{-2x+9}{6}\implies y=\stackrel{\stackrel{m}{\downarrow }}{-\cfrac{1}{3}}x+\cfrac{3}{2}\qquad \impliedby \qquad \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}{3}} ~\hfill \stackrel{reciprocal}{\cfrac{3}{-1}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{3}{-1} \implies \text{\LARGE 3}}}`