Question

line r has a slope of \\(\frac{7}{5}\\). 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

Perpendicular lines have slopes that are negative reciprocals. So if slope of line \( r \) is \( m_1 \), slope of line \( s \) (\( m_2 \)) is \( m_2 = -\frac{1}{m_1} \).

Step2: Apply the rule to given slope

Given \( m_1=\frac{7}{5} \), then \( m_2 = -\frac{1}{\frac{7}{5}} \). Simplify \( -\frac{1}{\frac{7}{5}}=-\frac{5}{7} \) (by multiplying numerator and denominator by 5's reciprocal).

Answer:

\(-\frac{5}{7}\)