Given two points A (-5, 2) and B (1, -4), find :
 slope of AB.

Answer

To find the slope of the line segment AB given the points A (-5, 2) and B (1, -4), we will use the formula for the slope of a line between two points. The formula for the slope (m) is:

\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]

where \( (x_1, y_1) \) are the coordinates of point A and \( (x_2, y_2) \) are the coordinates of point B.

### Step-by-Step Solution:

1. **Identify the coordinates of points A and B:**
- Point A: \( (x_1, y_1) = (-5, 2) \)
- Point B: \( (x_2, y_2) = (1, -4) \)

2. **Substitute the coordinates into the slope formula:**
\[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-4 - 2}{1 - (-5)} \]

3. **Calculate the differences:**
- Calculate \( y_2 - y_1 \):
\[ -4 - 2 = -6 \]
- Calculate \( x_2 - x_1 \):
\[ 1 - (-5) = 1 + 5 = 6 \]

4. **Substitute the calculated values back into the slope formula:**
\[ m = \frac{-6}{6} \]

5. **Simplify the fraction:**
\[ m = -1 \]

### Final Answer:
The slope of the line segment AB is \( -1 \).