Point A and B have co-ordinates (7, -3) and (1,9) respectively. Find :
the slope of AB. 

Answer

To find the slope of the line segment AB that connects the points A(7, -3) and B(1, 9), we can use the formula for the slope of a line given two points \((x_1, y_1)\) and \((x_2, y_2)\):

\[ \text{slope} (m) = \frac{y_2 - y_1}{x_2 - x_1} \]

### Step-by-Step Solution:

1. **Identify the coordinates of points A and B**:
- Point A has coordinates \((x_1, y_1) = (7, -3)\)
- Point B has coordinates \((x_2, y_2) = (1, 9)\)

2. **Substitute the coordinates into the slope formula**:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{9 - (-3)}{1 - 7} \]

3. **Calculate \(y_2 - y_1\)**:
\[ y_2 - y_1 = 9 - (-3) = 9 + 3 = 12 \]

4. **Calculate \(x_2 - x_1\)**:
\[ x_2 - x_1 = 1 - 7 = -6 \]

5. **Substitute these values back into the slope formula**:
\[ m = \frac{12}{-6} \]

6. **Simplify the fraction**:
\[ m = -2 \]

### Final Answer:
The slope of the line segment AB is \(-2\).

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