Question

line a passes through points (-90, -3) and (-93, 92). line b is perpendicular to a. what is the slope of line b? simplify your answer and write it as a proper fraction, improper fraction, or integer.

Explanation:

Step1: Find slope of line a

Use slope formula \( m = \frac{y_2 - y_1}{x_2 - x_1} \). For points \((-90, -3)\) and \((-93, 92)\), \( x_1=-90, y_1=-3, x_2=-93, y_2=92 \).
\( m_a = \frac{92 - (-3)}{-93 - (-90)} = \frac{95}{-3} = -\frac{95}{3} \).

Step2: Find slope of line b (perpendicular)

Perpendicular slopes: \( m_b = -\frac{1}{m_a} \). Substitute \( m_a = -\frac{95}{3} \):
\( m_b = -\frac{1}{-\frac{95}{3}} = \frac{3}{95} \).

Answer:

\(\frac{3}{95}\)