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The problem asks for the equation of a line that is perpendicular to the line \( y = 4 \) and passes through the point \((-2, 5)\).

### Step-by-Step Solution:

1. **Identify the properties of the given line**:
   - The equation \( y = 4 \) is a horizontal line because it has a constant \( y \)-value.
   - Horizontal lines have a slope of 0.

2. **Determine the slope of the perpendicular line**:
   - Lines that are perpendicular to horizontal lines must be vertical. 
   - Vertical lines have undefined slopes, and their equations are of the form \( x = \text{constant} \).

3. **Find the equation of the perpendicular line**:
   - Since the line passes through the point \((-2, 5)\), the equation of the line is \( x = -2 \) because vertical lines are defined by a constant \( x \)-value.

Thus, the correct answer is option **D: \( x = -2 \)**.

Would you like more details or have any questions?

Here are some related questions you might want to explore:

1. What is the equation of a line perpendicular to \( y = -3 \) through point \( (2, 1) \)?
2. How do you determine if two lines are perpendicular based on their slopes?
3. What are the properties of vertical and horizontal lines in the coordinate plane?
4. How do you find the equation of a line given a point and a slope?
5. What is the difference between parallel and perpendicular lines in terms of slope?

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

Which one of the following equations of a line is perpendicular to the line y = 4 and travels through the point (-2, 5)?

Learn how to determine the equation of a line that is perpendicular to y = 4 and passes through the point (-2, 5). This problem covers key geometry concepts such as perpendicular lines, vertical and horizontal lines, and slope properties. Suitable for students in Grades 9-10.

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