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 $\frac{1}{8}$.

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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!