Question

a parallel
b perpendicular
c neither

Explanation:

Step1: Find slope of line \(a\)

Let two - points on line \(a\) be \((- 4,8)\) and \((0,-4)\). The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). So, \(m_a=\frac{-4 - 8}{0+4}=\frac{-12}{4}=-3\).

Step2: Find slope of line \(b\)

Let two - points on line \(b\) be \((2,6)\) and \((4,0)\). Using the slope formula \(m=\frac{y_2 - y_1}{x_2 - x_1}\), we have \(m_b=\frac{0 - 6}{4 - 2}=\frac{-6}{2}=-3\).

Step3: Determine the relationship

Parallel lines have equal slopes. Since \(m_a=-3\) and \(m_b=-3\), the two lines are parallel.

Answer:

A. Parallel