Question

line g has a slope of \\(\frac{3}{5}\\). line h is perpendicular to g. what is the slope of line h? 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: Calculate the slope of line h

Given the slope of line \( g \) is \( \frac{3}{5} \), then the slope of line \( h \) (perpendicular to \( g \)) is the negative reciprocal of \( \frac{3}{5} \). The reciprocal of \( \frac{3}{5} \) is \( \frac{5}{3} \), and the negative of that is \( -\frac{5}{3} \).

Answer:

\( -\frac{5}{3} \)