graph the line that is perpendicular to the line x=-4 and that passes through the point (5,5). Write the equation of the perpendicular.

The line \( x = -4 \) is a vertical line, meaning it has an undefined slope. Any line that is perpendicular to a vertical line is a horizontal line, which has a slope of 0.

The equation of a horizontal line passing through a point \( (x_1, y_1) \) is given by \( y = y_1 \).

Since the line passes through the point \( (5, 5) \), the equation of the perpendicular line is:

\[
y = 5
\]

### Graph of the Line

- The original vertical line \( x = -4 \) is a vertical line passing through \( x = -4 \).
- The perpendicular line \( y = 5 \) is a horizontal line passing through the point \( (5, 5) \) and extending horizontally.

Would you like me to graph this for you?

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Here are five questions that expand on this concept:

1. What is the slope of a vertical line, and why is it undefined?
2. How can you determine if two lines are perpendicular in general?
3. How would the equation of the perpendicular line change if the point was \( (3, 7) \)?
4. What is the equation of a line parallel to \( x = -4 \) that passes through \( (1, 2) \)?
5. How do you find the equation of a line given a point and a slope?

**Tip:** When dealing with perpendicular lines, remember that the product of their slopes is always \( -1 \), unless one is vertical and the other is horizontal.

Graph the line that is perpendicular to the line x=-4 and that passes through the point (5,5). Write the equation of the perpendicular.

Learn how to find the equation of a line that is perpendicular to the vertical line x = -4 and passes through the point (5, 5). This problem focuses on key concepts of coordinate geometry, including the relationship between perpendicular lines and horizontal/vertical lines. Suitable for students in Grades 8-10.

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