Question

line q has a slope of \\(\frac{-4}{9}\\). line r is perpendicular to q. what is the slope of line r? simplify your answer and write it as a proper fraction, improper fraction, or integer.

Explanation:

Step1: Recall the rule for perpendicular slopes

The slopes of two perpendicular lines are negative reciprocals of each other. That is, if the slope of one line is \( m \), the slope of the line perpendicular to it is \( -\frac{1}{m} \).

Step2: Find the negative reciprocal of \( \frac{-4}{9} \)

First, find the reciprocal of \( \frac{-4}{9} \), which is \( \frac{9}{-4} \) or \( -\frac{9}{4} \). Then, take the negative of that reciprocal. The negative of \( -\frac{9}{4} \) is \( \frac{9}{4} \).

Answer:

\( \frac{9}{4} \)