Find the slope of the line perpendicular to AB if :
`A = (0, -5) and B = (-2, 4)`

Answer

To find the slope of the line perpendicular to line AB given the points A(0, -5) and B(-2, 4), we will follow these steps:

### Step 1: Find the slope of line AB
The formula for the slope (m) between two points (x1, y1) and (x2, y2) is given by:

\[ m = \frac{y2 - y1}{x2 - x1} \]

For points A(0, -5) and B(-2, 4):
- Let \( A = (x_1, y_1) = (0, -5) \)
- Let \( B = (x_2, y_2) = (-2, 4) \)

Substituting the coordinates into the slope formula:

\[ m_{AB} = \frac{4 - (-5)}{-2 - 0} = \frac{4 + 5}{-2} = \frac{9}{-2} = -\frac{9}{2} \]

### Step 2: Find the slope of the line perpendicular to AB
If two lines are perpendicular, the product of their slopes is -1. Let \( m_2 \) be the slope of the line perpendicular to AB. Therefore, we have:

\[ m_{AB} \cdot m_2 = -1 \]

Substituting the value of \( m_{AB} \):

\[ -\frac{9}{2} \cdot m_2 = -1 \]

### Step 3: Solve for \( m_2 \)
To find \( m_2 \), we can rearrange the equation:

\[ m_2 = \frac{-1}{-\frac{9}{2}} = \frac{2}{9} \]

### Conclusion
The slope of the line perpendicular to line AB is:

\[ \boxed{\frac{2}{9}} \]