Question

line d has a slope of \\(\frac{9}{8}\\). line e is perpendicular to d. what is the slope of line e? 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 \( d \) is \( m_d \), slope of \( e \) (\( m_e \)) is \( -\frac{1}{m_d} \).

Step2: Apply the rule to given slope

Given \( m_d = \frac{9}{8} \), then \( m_e = -\frac{1}{\frac{9}{8}} \). Simplify \( -\frac{1}{\frac{9}{8}} = -\frac{8}{9} \) (by multiplying numerator and denominator by 8, or using reciprocal property).

Answer:

\(-\frac{8}{9}\)