Question

Line Equation Line A y= 2x −3y= 2x −3 Line B y= 2x + 5y= 2x + 5 Line C y= −12x −2y= −12x −2 Line D y= 12x + 2y= 12x + 2 Given the linear equation in the table, which of the following statements is true? (1 point) Responses Line A is perpendicular to line B. Line A is perpendicular to line B. 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 C is perpendicular to line D.

Answer 1

To determine whether the lines are perpendicular, we need to find the slopes of each line from their equations.

1. **Line A:**
\( y = 2x - 3 \)
- Slope (\( m_A \)) = 2

2. **Line B:**
\( y = 2x + 5 \)
- Slope (\( m_B \)) = 2

3. **Line C:**
\( y = -12x - 2 \)
- Slope (\( m_C \)) = -12

4. **Line D:**
\( y = 12x + 2 \)
- Slope (\( m_D \)) = 12

Now, lines are perpendicular if the product of their slopes is -1.
Let's check each pair:

- **Line A and Line B:**
\( m_A \times m_B = 2 \times 2 = 4 \) (Not perpendicular)

- **Line B and Line D:**
\( m_B \times m_D = 2 \times 12 = 24 \) (Not perpendicular)

- **Line A and Line C:**
\( m_A \times m_C = 2 \times (-12) = -24 \) (Not perpendicular)

- **Line C and Line D:**
\( m_C \times m_D = (-12) \times 12 = -144 \) (Not perpendicular)

Since none of the pairs produce a product of -1, none of the lines are perpendicular to each other.

Therefore, none of the provided statements are true.