For each pair of linear equations given below, drawn graphs and then state, whether the lines drawn are parallel or perpendicular to each other.
`y=3x-1`
`y=3x+2`

Answer

To determine whether the lines represented by the equations \( y = 3x - 1 \) and \( y = 3x + 2 \) are parallel or perpendicular, we will follow these steps:

### Step 1: Identify the slopes of the lines
The general form of a linear equation is \( y = mx + b \), where \( m \) is the slope.

For the first equation \( y = 3x - 1 \):
- The slope \( m_1 = 3 \).

For the second equation \( y = 3x + 2 \):
- The slope \( m_2 = 3 \).

### Step 2: Compare the slopes
To determine if the lines are parallel or perpendicular:
- **Parallel Lines**: If the slopes are equal, the lines are parallel.
- **Perpendicular Lines**: If the product of the slopes is -1, the lines are perpendicular.

Here, both slopes are equal:
- \( m_1 = m_2 = 3 \).

Since the slopes are equal, the lines are parallel.

### Step 3: Conclusion
The lines represented by the equations \( y = 3x - 1 \) and \( y = 3x + 2 \) are parallel to each other.

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