Question

Use the table to answer the question.Line EquationLine A y=2x−3 Line B y=2x+5 Line  C y=−12x−2 Line  D y=12x+2 Given the linear equations in the table, which of the following statements is true?(1 point)ResponsesLine A is perpendicular to line B.Line  upper A is perpendicular to line upper B .Line A is perpendicular to line C.Line  upper A is perpendicular to line upper C .Line C is perpendicular to line D.Line  upper C is perpendicular to line upper D .Line B is perpendicular to line D.Line  upper B is perpendicular to line upper D .

Answer 1

To determine which lines are perpendicular to each other, we need to look at the slopes of the lines given by their equations.

1. **Identify the slopes:**
- Line A: \( y = 2x - 3 \) (slope = 2)
- Line B: \( y = 2x + 5 \) (slope = 2)
- Line C: \( y = -12x - 2 \) (slope = -12)
- Line D: \( y = 12x + 2 \) (slope = 12)

2. **Check for perpendicularity:**
- Two lines are perpendicular if the product of their slopes is -1 (i.e., if one slope is the negative reciprocal of the other).

- **Line A and Line B:**
- Slopes: 2 and 2
- \( 2 \times 2 = 4 \) (not perpendicular)

- **Line A and Line C:**
- Slopes: 2 and -12
- \( 2 \times -12 = -24 \) (not perpendicular)

- **Line C and Line D:**
- Slopes: -12 and 12
- \( -12 \times 12 = -144 \) (not perpendicular)

- **Line B and Line D:**
- Slopes: 2 and 12
- \( 2 \times 12 = 24 \) (not perpendicular)

3. **Conclusion:**
Since none of the pairs of lines have slopes that are negative reciprocals of each other, there are no perpendicular lines among the given options.

Thus, the correct answer is: **None of the statements are true regarding perpendicular lines.**