Question

Line g passes through points (5, 1) and (9, 6). Line his perpendicular to g. What is the slope

of line h?
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 G

`(\stackrel{x_1}{5}~,~\stackrel{y_1}{1})\qquad (\stackrel{x_2}{9}~,~\stackrel{y_2}{6})~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{6}-\stackrel{y1}{1}}}{\underset{run} {\underset{x_2}{9}-\underset{x_1}{5}}} \implies \cfrac{5}{4}`

with that in mind, let's check for H's slope

`\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{\cfrac{5}{4}} ~\hfill \stackrel{reciprocal}{\cfrac{4}{5}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{4}{5}}}`

Answer 2

The slope of the points given =5/4.
Perpendicular slope is opposite reciprocal therefore the answer is -4/5