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To find the equations for the vertical and horizontal lines passing through the point \((-8, 1)\):

1. **Vertical Line**: A vertical line passing through a point will always have an equation in the form \( x = a \), where \( a \) is the x-coordinate of the point. For the point \((-8, 1)\), the x-coordinate is \(-8\).
   
   So, the equation for the vertical line is:
   \[
   x = -8
   \]

2. **Horizontal Line**: A horizontal line passing through a point will always have an equation in the form \( y = b \), where \( b \) is the y-coordinate of the point. For the point \((-8, 1)\), the y-coordinate is \(1\).

   Therefore, the equation for the horizontal line is:
   \[
   y = 1
   \]

To summarize:

- Vertical line: \( x = -8 \)
- Horizontal line: \( y = 1 \)

Would you like a further explanation or have any questions?

Here are some related questions:
1. What would the equations be for lines passing through different points?
2. How can we determine the slope of vertical and horizontal lines?
3. Why do vertical lines have an undefined slope?
4. How can these equations be visualized on a coordinate plane?
5. How does the form of the line equation change for diagonal lines?

**Tip**: Vertical lines have constant \(x\)-values, while horizontal lines have constant \(y\)-values.

Write equations for the vertical and horizontal lines passing through the point (-8, 1).

Learn how to write equations for the vertical and horizontal lines passing through the point (-8, 1). Understand the key concepts of coordinate geometry and line equations in this step-by-step solution. Suitable for middle school students in Grades 6-8.

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