Question

line m has a slope of \\(\frac{-4}{9}\\). line n is perpendicular to m. what is the slope of line n? simplify your answer and write it as a proper fraction, improper fraction, or integer.

Explanation:

Step1: Recall perpendicular slope rule

The slopes of two perpendicular lines are negative reciprocals. So if slope of line \( m \) is \( m_1 \), slope of line \( n \) (perpendicular to \( m \)) is \( m_2 = -\frac{1}{m_1} \).

Step2: Apply the rule to given slope

Given slope of line \( m \) is \( \frac{-4}{9} \). Then the slope of line \( n \) is the negative reciprocal, so we take the reciprocal of \( \frac{-4}{9} \) which is \( \frac{9}{-4} \) and then take the negative of that. The negative of \( \frac{9}{-4} \) is \( \frac{9}{4} \).

Answer:

\(\frac{9}{4}\)