Final answer:
To determine if two lines are parallel, perpendicular, or neither, compare their slopes. If the slopes are equal, the lines are parallel. If the slopes are negative reciprocals, the lines are perpendicular. Otherwise, the lines are neither parallel nor perpendicular.
Step-by-step explanation:
To determine if two lines are parallel, perpendicular, or neither, we need to compare their slopes. The first line can be rewritten as y = 3x + 6, so its slope is 3. The second line can be rewritten as 11x - 4y = -14, which simplifies to y = (11/4)x + (14/4), so its slope is 11/4. Since the slopes are not equal and not negative reciprocals, the lines are neither parallel nor perpendicular.
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