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To solve the questions given, let's examine the line equation provided:

The equation is:
\[
y = -x + 8
\]

In this equation, the slope (\( m \)) of the line is the coefficient of \( x \). Thus, the slope \( m \) is:
\[
m = -1
\]

### 1. Slope of a Parallel Line
For a line to be parallel to another, it must have the same slope. Therefore, the slope of a line parallel to \( y = -x + 8 \) is also:
\[
m = -1
\]

### 2. Slope of a Perpendicular Line
For a line to be perpendicular to another, its slope must be the negative reciprocal of the original line’s slope. The negative reciprocal of \(-1\) is:
\[
m = 1
\]

### Summary
- **Slope of a perpendicular line:** \( 1 \)
- **Slope of a parallel line:** \( -1 \)

Would you like more details, or do you have any questions?

Here are five related questions that expand on this topic:
1. How do you find the equation of a line that passes through a specific point and is parallel to \( y = -x + 8 \)?
2. How would you write the equation of a line perpendicular to \( y = -x + 8 \) passing through a given point?
3. What is the relationship between slopes of parallel and perpendicular lines in general?
4. If a line has an undefined slope, what are the slopes of lines parallel and perpendicular to it?
5. How would you find the intersection point of two lines with given slopes and y-intercepts?

**Tip:** Remember, parallel lines share the same slope, while perpendicular lines have slopes that are negative reciprocals of each other.

Consider the line y = -x + 8. What is the slope of a line perpendicular to this line? What is the slope of a line parallel to this line?

Learn how to find the slopes of lines parallel and perpendicular to y = -x + 8. Understand the concepts of parallel and perpendicular slopes and apply the slope-intercept form in this problem, suitable for students in Grades 8-10.

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