Question

Identify if the following lines are parallel, perpendicular, or neither(2 points) y=6x+1y=6x+1 and y=−16x+3y=−16x+3 y=3x+4y=3x+4 and y=3x−1y=3x−1 y=−2x−5y=−2x−5 and y=−12x+8y=−12x+8

Answer 1

To determine if the lines are parallel, perpendicular, or neither, we need to analyze the slopes of the lines.

1. For the lines \( y = 6x + 1 \) and \( y = -16x + 3 \):
- The slope of the first line \( y = 6x + 1 \) is **6**.
- The slope of the second line \( y = -16x + 3 \) is **-16**.
- Since the product of these slopes \( (6) \times (-16) = -96 \), the lines are **perpendicular**.

2. For the lines \( y = 3x + 4 \) and \( y = 3x - 1 \):
- The slope of the first line \( y = 3x + 4 \) is **3**.
- The slope of the second line \( y = 3x - 1 \) is also **3**.
- Since the slopes are equal, the lines are **parallel**.

3. For the lines \( y = -2x - 5 \) and \( y = -12x + 8 \):
- The slope of the first line \( y = -2x - 5 \) is **-2**.
- The slope of the second line \( y = -12x + 8 \) is **-12**.
- Since the product of these slopes \( (-2) \times (-12) = 24 \) which is positive, the lines are **neither parallel nor perpendicular**.

In summary:
1. \( y = 6x + 1 \) and \( y = -16x + 3 \) → **Perpendicular**
2. \( y = 3x + 4 \) and \( y = 3x - 1 \) → **Parallel**
3. \( y = -2x - 5 \) and \( y = -12x + 8 \) → **Neither**