Find the slope of a line perpendicular to the line whose slope is 0

Answer

To find the slope of a line that is perpendicular to a line with a slope of 0, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the slope of the given line**:
The slope of the given line is \( m_1 = 0 \).

2. **Use the property of perpendicular lines**:
For two lines to be perpendicular, the product of their slopes must equal -1. This can be expressed as:
\[ m_1 \cdot m_2 = -1 \]
where \( m_1 \) is the slope of the first line and \( m_2 \) is the slope of the line that is perpendicular to it.

3. **Substitute the known slope into the equation**:
We substitute \( m_1 = 0 \) into the equation:
\[ 0 \cdot m_2 = -1 \]

4. **Solve for \( m_2 \)**:
The equation simplifies to:
\[ 0 = -1 \]
This equation does not hold true. Therefore, we need to analyze what it means for \( m_2 \).

5. **Interpret the result**:
Since the slope \( m_1 = 0 \) indicates a horizontal line, a line that is perpendicular to a horizontal line must be a vertical line. The slope of a vertical line is considered to be undefined or can be thought of as approaching infinity.

### Conclusion:
Thus, the slope of a line that is perpendicular to a line with a slope of 0 is **undefined** or can be described as **infinity**.