Question

Line a passes through points (1, 18) and (9, 9). Line b is perpendicular to a. What is the slope of line b?

Simplify your answer and write it as a proper fraction, improper fraction, or integer.

Answer 1

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

`(\stackrel{x_1}{1}~,~\stackrel{y_1}{18})\qquad (\stackrel{x_2}{9}~,~\stackrel{y_2}{9}) ~\hfill~ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{9}-\stackrel{y1}{18}}}{\underset{\textit{\large run}} {\underset{x_2}{9}-\underset{x_1}{1}}} \implies \cfrac{ -9 }{ 8 } \implies \stackrel{ \textit{\LARGE A} }{-\cfrac{9}{8}} \\\\[-0.35em] ~\dotfill`

`\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{ \cfrac{-9}{8}} ~\hfill \stackrel{reciprocal}{\cfrac{8}{-9}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{8}{-9} \implies \cfrac{8}{ 9 } ~~ \textit{\LARGE B}}}`