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To solve this problem, we need to find the slope of a line that is perpendicular to the given line \( y = -8x + 12 \).

1. **Identify the slope of the given line**: 
   The equation of the given line is in slope-intercept form, \( y = mx + b \), where \( m \) is the slope. For the given equation \( y = -8x + 12 \), the slope \( m \) is \( -8 \).

2. **Determine the slope of the perpendicular line**: 
   For two lines to be perpendicular, the product of their slopes must be \( -1 \). If the slope of the original line is \( m_1 \), the slope of the perpendicular line \( m_2 \) is found using the relation:
   \[
   m_1 \times m_2 = -1
   \]
   Since the slope of the given line is \( -8 \), we can solve for \( m_2 \):
   \[
   -8 \times m_2 = -1
   \]
   Dividing both sides by \( -8 \):
   \[
   m_2 = \frac{1}{8}
   \]

Thus, the slope of the line perpendicular to \( y = -8x + 12 \) is \( \frac{1}{8} \).

Do you want more details on this solution or have any other questions?

Here are 5 related questions:
1. What is the slope of a line perpendicular to \( y = 3x + 5 \)?
2. How do you find the slope of a line parallel to another line?
3. What is the relationship between the slopes of parallel lines?
4. How do you write the equation of a line with a given slope and point?
5. What is the geometric interpretation of a line’s slope?

**Tip**: Remember, the slopes of perpendicular lines are negative reciprocals of each other!

What is the slope of a line perpendicular to y = -8x + 12?

Learn how to find the slope of a line perpendicular to y = -8x + 12. This problem covers key concepts in algebra such as linear equations, slope, and the relationship between perpendicular lines. Suitable for students in Grades 8-10.

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