What is the equation of a line parallel to x-axis at a distance of 5 units below x-axis?

Options

A. x =5
B. x = -5
C. y = 5
D. y = - 5

Answer

To find the equation of a line parallel to the x-axis that is located 5 units below the x-axis, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Position of the Line**:
- The x-axis is the horizontal line where the value of y is 0.
- A line parallel to the x-axis will have the same y-value for all points on that line.

2. **Determine the y-coordinate of the Line**:
- Since we need a line that is 5 units below the x-axis, we subtract 5 from the y-coordinate of the x-axis (which is 0).
- Therefore, the y-coordinate of our line will be:
\[ y = 0 - 5 = -5 \]

3. **Write the Equation of the Line**:
- The equation of a line parallel to the x-axis at a specific y-coordinate is given by:
\[ y = k \]
- In this case, since we found that the y-coordinate is -5, the equation of the line is:
\[ y = -5 \]

### Final Answer:
The equation of the line parallel to the x-axis at a distance of 5 units below the x-axis is:
\[ y = -5 \]