To determine if two lines are perpendicular, we can use the slopes of the lines from their equations in the form \( y = mx + b \), where \( m \) is the slope. Two lines are perpendicular if the product of their slopes is -1.
Let's identify the slopes of each line:
- Line A: \( y = -12x - 2 \) → slope \( m_A = -12 \)
- Line B: \( y = 2x - 3 \) → slope \( m_B = 2 \)
- Line C: \( y = 12x + 2 \) → slope \( m_C = 12 \)
- Line D: \( y = 2x + 5 \) → slope \( m_D = 2 \)
Now we can check for perpendicularity:
- Line A and Line B: \( m_A \times m_B = -12 \times 2 = -24 \) (not perpendicular)
- Line A and Line C: \( m_A \times m_C = -12 \times 12 = -144 \) (not perpendicular)
- Line C and Line D: \( m_C \times m_D = 12 \times 2 = 24 \) (not perpendicular)
- Line B and Line D: \( m_B \times m_D = 2 \times 2 = 4 \) (not perpendicular)
None of the line pairs here are perpendicular.
Therefore, the correct response is that none of the given pairs of lines are perpendicular.