Question

Given the table below, which of the following statements is true?

Line Equation
Line A y=−12x−2

Line B y=2x−3

Line C y=12x+2

Line D y=2x+5




(1 point)
Responses which answer is correct and why

Line C is perpendicular to Line D
Line C is perpendicular to Line D

Line B is perpendicular to Line D
Line B is perpendicular to Line D

Line A is perpendicular to Line C
Line A is perpendicular to Line C

Line A is perpendicular to Line B

Answer 1

To determine which of the statements is true, we need to analyze the slopes of the lines provided in the equations.

The general form of a linear equation is \(y = mx + b\), where \(m\) is the slope. Two lines are perpendicular if the product of their slopes is \(-1\).

Here are the slopes of each line:

- **Line A:** \(y = -12x - 2\)
**Slope of Line A (m_A)** = -12

- **Line B:** \(y = 2x - 3\)
**Slope of Line B (m_B)** = 2

- **Line C:** \(y = 12x + 2\)
**Slope of Line C (m_C)** = 12

- **Line D:** \(y = 2x + 5\)
**Slope of Line D (m_D)** = 2

Now, let’s check each statement:

1. **Line C is perpendicular to Line D:**
- Slopes: m_C = 12, m_D = 2
- \(12 * 2 \neq -1\) (not perpendicular)

2. **Line B is perpendicular to Line D:**
- Slopes: m_B = 2, m_D = 2
- \(2 * 2 \neq -1\) (not perpendicular)

3. **Line A is perpendicular to Line C:**
- Slopes: m_A = -12, m_C = 12
- \((-12) * 12 = -144 \neq -1\) (not perpendicular)

4. **Line A is perpendicular to Line B:**
- Slopes: m_A = -12, m_B = 2
- \((-12) * 2 = -24 \neq -1\) (not perpendicular)

Since all calculations show that none of the pairs of lines listed in the options are perpendicular to each other, it appears that the correct answer must be none of the given options.

However, please ensure to verify the conditions of perpendicularity result in slopes multiplying to -1 for correct evaluation in your context. If the options have been misinterpreted or are waiting for a distinct true statement, please clarify or provide any additional context for re-evaluation.