find the slope of a line that is a. parallel and b. perpendicular to the line with the given equation x = -8

The given equation \( x = -8 \) represents a vertical line on the Cartesian plane. The key characteristics of this line are:

1. It passes through all points where the x-coordinate is \(-8\).
2. It has an undefined slope because the rise/run ratio is infinite (as the line does not run horizontally at all).

**a. Slope of a line parallel to \( x = -8 \)**:  
A line parallel to \( x = -8 \) would also be a vertical line. Therefore, its slope is also **undefined**.

**b. Slope of a line perpendicular to \( x = -8 \)**:  
A line perpendicular to a vertical line is a horizontal line. The slope of any horizontal line is \(0\).

Would you like more details on how these conclusions are drawn? Here are some additional questions to explore:

1. What is the general equation of a vertical line?
2. How do you find the slope of a line given two points on the line?
3. What does it mean for two lines to be parallel in terms of their slopes?
4. How can the slope-intercept form of a line be useful in understanding slope?
5. What is the relationship between the slopes of perpendicular lines?
6. How does the concept of slope apply to non-linear functions?
7. What are some examples of real-world situations where understanding slope is important?
8. How can graphing lines help in visualizing their slopes?

**Tip:** When identifying the slope of a line, remember that vertical lines have an undefined slope, while horizontal lines have a slope of zero.

Understand how to find the slope of lines parallel and perpendicular to the equation x = -8. Explore the concept of slope in geometry, including vertical and horizontal lines. Suitable for high school students studying geometry and algebra.

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