Raul graphed a line on the coordinate plane.
 


What is the equation of the line and its relationship to the y-axis?
A.y = ‒6, and the line is parallel to the y-axis.
B.y = ‒6, and the line is perpendicular to y-axis.
C.x = ‒6, and the line is parallel to the y-axis.
D.x = ‒6, and the line is perpendicular to y-axis.

To determine the correct answer, let's understand the properties of lines described by equations involving \( x \) and \( y \).

### Analysis:

1. **Equation of the line:**  
   - An equation in the form \( y = \text{constant} \) represents a horizontal line.  
   - An equation in the form \( x = \text{constant} \) represents a vertical line.

2. **Relationship with the y-axis:**  
   - A line parallel to the y-axis is a vertical line, described by \( x = \text{constant} \).  
   - A line perpendicular to the y-axis is a horizontal line, described by \( y = \text{constant} \).

### Option Analysis:

- **Option A: \( y = -6 \), and the line is parallel to the y-axis.**  
  This describes a horizontal line, which is incorrect since it is not parallel but perpendicular to the y-axis.

- **Option B: \( y = -6 \), and the line is perpendicular to the y-axis.**  
  This correctly describes a horizontal line that is perpendicular to the y-axis.

- **Option C: \( x = -6 \), and the line is parallel to the y-axis.**  
  This describes a vertical line, which is parallel to the y-axis.

- **Option D: \( x = -6 \), and the line is perpendicular to the y-axis.**  
  This incorrectly describes the relationship since a vertical line cannot be perpendicular to the y-axis.

### Conclusion:
The correct option is:
**C. \( x = -6 \), and the line is parallel to the y-axis.**

Would you like further details or have any questions?

### Related Questions:
1. What does the equation \( x = 4 \) represent on the coordinate plane?
2. How do you determine the slope of a line parallel to the y-axis?
3. What is the slope of a line perpendicular to the x-axis?
4. How do you find the distance between a line \( x = a \) and another line \( x = b \)?
5. How can you find the point of intersection between a line \( x = -6 \) and \( y = -6 \)?

**Tip:** For any equation in the form \( x = \text{constant} \), the line will always be vertical and parallel to the y-axis.

Raul graphed a line on the coordinate plane.
What is the equation of the line and its relationship to the y-axis?
A. y = ‒6, and the line is parallel to the y-axis.
B. y = ‒6, and the line is perpendicular to y-axis.
C. x = ‒6, and the line is parallel to the y-axis.
D. x = ‒6, and the line is perpendicular to y-axis.

Explore how the equation x = -6 represents a line parallel to the y-axis. This problem demonstrates key concepts of coordinate geometry, including vertical and horizontal lines and their relationships with the axes. Suitable for students in Grades 8-10.

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