Question

Line u passes through points (5, 6) and (7, 9). Line v is perpendicular to u. What is the slope of line v?

Answer 1

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

`(\stackrel{x_1}{5}~,~\stackrel{y_1}{6})\qquad (\stackrel{x_2}{7}~,~\stackrel{y_2}{9}) ~\hfill~ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{9}-\stackrel{y1}{6}}}{\underset{\textit{\large run}} {\underset{x_2}{7}-\underset{x_1}{5}}} \implies \cfrac{ 3 }{ 2 } \\\\[-0.35em] ~\dotfill`

`\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 \underset{ \textit{\large Line V's slope} }{\stackrel{negative~reciprocal}{-\cfrac{2}{3} }}}`