Question

Consider the line 6x+4y=-5

Answer 1

$6x+4y=-5\implies 4y=-6x-5\implies y=\cfrac{-6x-5}{4} \\\\\\ y=-\cfrac{6x}{4}-\cfrac{5}{4}\implies y=\stackrel{\stackrel{m}{\downarrow }}{-\cfrac{3}{2}} x-\cfrac{5}{4}\qquad \impliedby \qquad \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}$

$\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{-\cfrac{3}{2}} ~\hfill \stackrel{reciprocal}{-\cfrac{2}{3}} ~\hfill \stackrel{negative~reciprocal}{-\left( -\cfrac{2}{3} \right)\implies \cfrac{2}{3}}} \\\\[-0.35em] ~\dotfill\\\\ \textit{and a \underline{parallel line} to this one will also have a slope of }-\cfrac{3}{2}$