Question

line f has a slope of \\(\frac{-6}{5}\\). line g is perpendicular to f. what is the slope of line g? simplify your answer and write it as a proper fraction, improper fraction, or integer.

Explanation:

Step1: Recall the slope of perpendicular lines

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 \( \frac{-6}{5} \)

Let the slope of line \( f \) be \( m_f = \frac{-6}{5} \). The slope of line \( g \) (perpendicular to \( f \)) \( m_g \) is the negative reciprocal of \( m_f \). First, find the reciprocal of \( \frac{-6}{5} \), which is \( \frac{5}{-6}=-\frac{5}{6} \). Then, take the negative of that reciprocal: \( -(-\frac{5}{6})=\frac{5}{6} \).

Answer:

\(\frac{5}{6}\)