Question

line r has a slope of \\(\frac{21}{64}\\). 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. If the slope of line \( r \) is \( m_r \), then the slope of line \( s \) (perpendicular to \( r \)) is \( m_s = -\frac{1}{m_r} \).

Step2: Identify the slope of line \( r \)

Given the slope of line \( r \) is \( \frac{21}{64} \).

Step3: Calculate the slope of line \( s \)

Using the formula for the slope of a perpendicular line, we substitute \( m_r = \frac{21}{64} \) into \( m_s = -\frac{1}{m_r} \).
\[
m_s = -\frac{1}{\frac{21}{64}} = -\frac{64}{21}
\]

Answer:

\( -\frac{64}{21} \)