Question

line r has a slope of \\(\frac{5}{4}\\). 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 perpendicular slope rule

For two perpendicular lines, the product of their slopes is -1. Let the slope of line \( r \) be \( m_r=\frac{5}{4} \) and the slope of line \( s \) be \( m_s \). Then \( m_r\times m_s=-1 \).

Step2: Solve for \( m_s \)

Substitute \( m_r = \frac{5}{4} \) into the equation: \( \frac{5}{4}\times m_s=-1 \). To find \( m_s \), divide both sides by \( \frac{5}{4} \), which is equivalent to multiplying by its reciprocal \( \frac{4}{5} \). So \( m_s=-1\times\frac{4}{5}=-\frac{4}{5} \).

Answer:

\(-\frac{4}{5}\)