Question

line f passes through points (1, 13) and (3, 8). line g is perpendicular to f. what is the slope of line g? simplify your answer and write it as a proper fraction, improper fraction, or integer.

Explanation:

Step1: Find slope of line f

Use slope formula \( m = \frac{y_2 - y_1}{x_2 - x_1} \). For points \((1, 13)\) and \((3, 8)\), \( m_f = \frac{8 - 13}{3 - 1} = \frac{-5}{2} \).

Step2: Find slope of line g (perpendicular)

Perpendicular slopes multiply to \(-1\). Let \( m_g \) be slope of g. Then \( m_f \times m_g = -1 \), so \( \frac{-5}{2} \times m_g = -1 \). Solve for \( m_g \): \( m_g = \frac{-1}{\frac{-5}{2}} = \frac{2}{5} \).

Answer:

\(\frac{2}{5}\)