Respuesta :
keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the equation above
[tex]12x-9y = 27\implies -9y=-12x+27\implies y=\cfrac{-12x+27}{-9} \\\\\\ y=\cfrac{-12x}{-9}+\cfrac{27}{-9}\implies y=\stackrel{\stackrel{m}{\downarrow }}{\cfrac{4}{3}}x-3\impliedby \begin{array}{|c|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}[/tex]
therefore
[tex]\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{\cfrac{4}{3}} ~\hfill \stackrel{reciprocal}{\cfrac{3}{4}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{3}{4}}}[/tex]
