Question

line 1 passes through (5, 2) and (5, 8)
line 2 passes through (- 1, 4) and (7, 4)

Explanation:

Step1: Find slope of Line 1

Slope formula: $m_1 = \frac{y_2 - y_1}{x_2 - x_1} = \frac{8-2}{5-5} = \frac{6}{0}$ (undefined, vertical line $x=5$)

Step2: Find slope of Line 2

Slope formula: $m_2 = \frac{y_2 - y_1}{x_2 - x_1} = \frac{4-4}{7-(-1)} = \frac{0}{8} = 0$ (horizontal line $y=4$)

Step3: Analyze line relationship

Vertical and horizontal lines are perpendicular.

Answer:

Line 1 is a vertical line $x=5$, Line 2 is a horizontal line $y=4$, so the two lines are perpendicular to each other.