Find the slope of a line perpendicular to the line which passes through each pair of the following points:
(0, 8) and (-5, 2)

Answer

To find the slope of a line that is perpendicular to the line passing through the points (0, 8) and (-5, 2), we can follow these steps:

### Step 1: Identify the points
Let the points be:
- \( (x_1, y_1) = (0, 8) \)
- \( (x_2, y_2) = (-5, 2) \)

### Step 2: Use the slope formula
The formula for the slope \( m \) of a line passing through two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]

### Step 3: Substitute the values
Substituting the values of the points into the slope formula:
\[ m_1 = \frac{2 - 8}{-5 - 0} \]

### Step 4: Calculate the slope
Now, calculate the values:
\[ m_1 = \frac{-6}{-5} = \frac{6}{5} \]

### Step 5: Find the slope of the perpendicular line
The slope of a line that is perpendicular to another line is the negative reciprocal of the slope of the original line. Therefore, if \( m_1 = \frac{6}{5} \), then the slope \( m_2 \) of the perpendicular line is:
\[ m_2 = -\frac{1}{m_1} = -\frac{1}{\frac{6}{5}} = -\frac{5}{6} \]

### Final Answer
Thus, the slope of the line perpendicular to the line passing through the points (0, 8) and (-5, 2) is:
\[ \boxed{-\frac{5}{6}} \]