Find the slope of a line perpendicular to the line whose slope is 5.

Answer

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

### Step-by-Step Solution:

1. **Identify the given slope**:
The slope of the given line is \( m_1 = 5 \).

2. **Understand the relationship between slopes of perpendicular lines**:
For two lines to be perpendicular, the product of their slopes must equal \(-1\). This can be expressed mathematically 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 perpendicular to it.

3. **Substitute the known slope into the equation**:
We know \( m_1 = 5 \). Therefore, we can substitute this value into the equation:
\[ 5 \cdot m_2 = -1 \]

4. **Solve for \( m_2 \)**:
To find \( m_2 \), we need to isolate it. We can do this by dividing both sides of the equation by 5:
\[ m_2 = \frac{-1}{5} \]

5. **Conclusion**:
The slope of the line that is perpendicular to the line with a slope of 5 is:
\[ m_2 = -\frac{1}{5} \]

### Final Answer:
The slope of the line perpendicular to the line whose slope is 5 is \(-\frac{1}{5}\).