Question

Identify if the following lines are parallel, perpendicular, or neither(2 points)
y=6x+1
and y=−16x+3

y=3x+4
and y=3x−1

y=−2x−5
and y=−12x+8

Answer 1

To determine if the given lines are parallel, perpendicular, or neither, we need to look at the slopes of the lines in each pair.

1. **Lines: \( y = 6x + 1 \) and \( y = -16x + 3 \)**
- Slope of the first line: \( m_1 = 6 \)
- Slope of the second line: \( m_2 = -16 \)
- Since \( m_1 \cdot m_2 = 6 \cdot (-16) = -96 \) (not equal to -1), the lines are **neither** parallel nor perpendicular.

2. **Lines: \( y = 3x + 4 \) and \( y = 3x - 1 \)**
- Slope of the first line: \( m_1 = 3 \)
- Slope of the second line: \( m_2 = 3 \)
- Since \( m_1 = m_2 \), the lines are **parallel**.

3. **Lines: \( y = -2x - 5 \) and \( y = -12x + 8 \)**
- Slope of the first line: \( m_1 = -2 \)
- Slope of the second line: \( m_2 = -12 \)
- Since \( m_1 \cdot m_2 = -2 \cdot (-12) = 24 \) (not equal to -1), the lines are **neither** parallel nor perpendicular.

In summary:
1. Neither
2. Parallel
3. Neither