Final answer:
Lines A (y = 3x + 2) and C (y = 3x + 4) are parallel to the line y=3x-16 due to having the same slope. Lines B (y = -2x - 16) and D (y = -3x - 16) are neither parallel nor perpendicular to the given line as their slopes do not meet the necessary conditions for either.
Step-by-step explanation:
To determine which lines are parallel, perpendicular, or neither parallel nor perpendicular to the line y=3x-16, we will compare their slopes. Two lines are parallel if they have equal slopes and perpendicular if the product of their slopes is -1.
- Line A: y = 3x + 2 has the same slope as the given line (slope=3), so they are parallel.
- Line B: y = -2x - 16 has a slope of -2. Since the product of the slopes (3*(-2)) is not -1, they are neither parallel nor perpendicular.
- Line C: y = 3x + 4 has the same slope as the given line (slope=3), making them parallel as well.
- Line D: y = -3x - 16 has a slope of -3. Since the product of the slopes (3*(-3)) equals -9 and not -1, they are neither parallel nor perpendicular.
So, lines A and C are parallel to the given line y=3x-16, while lines B and D are neither parallel nor perpendicular.