Question

line r has a slope of \\(\frac{5}{2}\\). line s is perpendicular to r. what is the slope of line s? 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 \(s\)

Given the slope of line \(r\) is \(\frac{5}{2}\), then the slope of line \(s\) (perpendicular to \(r\)) is the negative reciprocal of \(\frac{5}{2}\).
The reciprocal of \(\frac{5}{2}\) is \(\frac{2}{5}\), and the negative of that is \(-\frac{2}{5}\).

Answer:

\(-\frac{2}{5}\)