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To determine whether the lines are parallel, perpendicular, or neither, we need to analyze the slopes of the two lines. The equations given are:

1. \( y = 6x + 5 \)
2. \( y = 13x - 2 \)

### Step 1: Identify the slopes
Both equations are in slope-intercept form, \( y = mx + b \), where \( m \) represents the slope.

- The slope of the first line is \( m_1 = 6 \).
- The slope of the second line is \( m_2 = 13 \).

### Step 2: Determine the relationship between the slopes
- **Parallel lines** have equal slopes. For lines to be parallel, \( m_1 \) should equal \( m_2 \), but here \( 6 \neq 13 \), so the lines are not parallel.
  
- **Perpendicular lines** have slopes that are negative reciprocals of each other. This means \( m_1 \cdot m_2 = -1 \). In this case:
  \[
  6 \cdot 13 = 78 \quad (\text{not } -1),
  \]
  so the lines are not perpendicular either.

Since the lines are neither parallel nor perpendicular, the correct answer is:
- **B. neither**

Let me know if you'd like further details or have any questions! Here are some related questions:

1. What does it mean for two lines to be parallel in terms of slope?
2. How do we identify if lines are perpendicular using their slopes?
3. Can two lines be neither parallel nor perpendicular? What does that indicate?
4. How would you determine the slope if the equation wasn't in slope-intercept form?
5. What is the significance of the y-intercept in these equations?

**Tip:** Always make sure to compare slopes directly when determining if lines are parallel or perpendicular!

Determine whether the pair of lines is parallel, perpendicular, or neither. y = 6x + 5, y = 13x - 2

Explore how to determine whether two linear equations y = 6x + 5 and y = 13x - 2 are parallel, perpendicular, or neither. The solution involves analyzing the slopes of the lines using the slope-intercept formula. Suitable for students in Grades 8-10.

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