Question

1. if another line is perpendicular to the line shown on the graph, what must be its slope? a. b. \\(\frac{2}{5}\\) c. \\(\frac{5}{2}\\) d. \\(-\frac{2}{5}\\) \\(-\frac{5}{2}\\)

Explanation:

Step1: Find slope of given line

Choose two points on the line, e.g., \((-2, 3)\) and \((3, 1)\). Slope formula: \(m = \frac{y_2 - y_1}{x_2 - x_1}\).
\(m = \frac{1 - 3}{3 - (-2)} = \frac{-2}{5} = -\frac{2}{5}\).

Step2: Slope of perpendicular line

Perpendicular slopes: \(m_1 \cdot m_2 = -1\). Let \(m_1 = -\frac{2}{5}\), solve for \(m_2\):
\(m_2 = \frac{-1}{m_1} = \frac{-1}{-\frac{2}{5}} = \frac{5}{2}\).

Answer:

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