Find the slope of a line perpendicular to the line whose slope is
-5(1)/(7)`

Answer

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

### Step 1: Identify the given slope
The slope of the given line is:
\[ m_1 = -5 \times \frac{1}{7} \]
Calculating this gives:
\[ m_1 = -\frac{5}{7} \]

### Step 2: Use the property of perpendicular slopes
For two lines to be perpendicular, the product of their slopes must equal -1. If \( m_1 \) is the slope of the first line, and \( m_2 \) is the slope of the line perpendicular to it, we have:
\[ m_1 \times m_2 = -1 \]
Substituting the value of \( m_1 \):
\[ -\frac{5}{7} \times m_2 = -1 \]

### Step 3: Solve for \( m_2 \)
To find \( m_2 \), we can rearrange the equation:
\[ m_2 = \frac{-1}{-\frac{5}{7}} \]
This simplifies to:
\[ m_2 = \frac{7}{5} \]

### Conclusion
Thus, the slope of the line that is perpendicular to the line with slope \( -\frac{5}{7} \) is:
\[ m_2 = \frac{7}{5} \]