Question

Identify if the following lines are parallel, perpendicular, or neither(2 points) y=34x−3 and y=34x+3 y=2x−4 and y=−2x+5 y=35x+5 and y=−53x+2

Answer 1

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

1. **Line 1: \( y = 34x - 3 \)**
- Slope (m₁) = 34

**Line 2: \( y = 34x + 3 \)**
- Slope (m₂) = 34
- Since the slopes are equal \( (m₁ = m₂) \), the lines are **parallel**.

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2. **Line 1: \( y = 2x - 4 \)**
- Slope (m₁) = 2

**Line 2: \( y = -2x + 5 \)**
- Slope (m₂) = -2
- The product of the slopes is \( m₁ \cdot m₂ = 2 \cdot (-2) = -4 \) which is negative. Since the slopes are negative reciprocals of each other, the lines are **perpendicular**.

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3. **Line 1: \( y = 35x + 5 \)**
- Slope (m₁) = 35

**Line 2: \( y = -53x + 2 \)**
- Slope (m₂) = -53
- The product of the slopes is \( m₁ \cdot m₂ = 35 \cdot (-53) = -1855 \) which is negative, but they are not negative reciprocals. Therefore, the lines are **neither parallel nor perpendicular**.

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**Summary:**
1. Lines \( y = 34x - 3 \) and \( y = 34x + 3 \): **Parallel**
2. Lines \( y = 2x - 4 \) and \( y = -2x + 5 \): **Perpendicular**
3. Lines \( y = 35x + 5 \) and \( y = -53x + 2 \): **Neither**