Choice B is the correct answer. Both equations are in slope-intercept form $y = mx + b$.

Analysis:

• First line: slope $m_1 = -3$, y-intercept $b_1 = 4$
• Second line: slope $m_2 = -3$, y-intercept $b_2 = -2$

Comparison:

• $m_1 = m_2 = -3$ → same slope
• $b_1 \ eq b_2$ → different y-intercepts

When lines have the same slope but different y-intercepts, they are parallel.

💡 Strategic Tip:

• Parallel lines: same slope, different intercepts
• Perpendicular lines: slopes are negative reciprocals ($m_1 \cdot m_2 = -1$)
• Identical lines: same slope AND same intercept

Choice A is incorrect because perpendicular lines have slopes that multiply to $-1$. Here, $(-3) \times (-3) = 9 \ eq -1$.

Choice C is incorrect because identical lines must have the same y-intercept.

Choice D is incorrect because parallel lines never intersect.