Find the slope and the inclination of the line AB if :
`A = (0, -sqrt(3))` and `B = (3, 0)`.

Answer

To find the slope and inclination of the line AB given the points A and B, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the coordinates of points A and B:**
- Point A = (0, -√3)
- Point B = (3, 0)

2. **Use the formula for the slope (m) of a line through two points:**
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Here, we can assign:
- \( (x_1, y_1) = (0, -\sqrt{3}) \) (Point A)
- \( (x_2, y_2) = (3, 0) \) (Point B)

3. **Substitute the coordinates into the slope formula:**
\[ m = \frac{0 - (-\sqrt{3})}{3 - 0} \]
Simplifying this gives:
\[ m = \frac{0 + \sqrt{3}}{3} = \frac{\sqrt{3}}{3} \]

4. **Simplify the slope:**
The slope \( m \) can be expressed as:
\[ m = \frac{\sqrt{3}}{3} \]

5. **Relate the slope to the angle of inclination:**
We know that the slope \( m \) is equal to \( \tan(\theta) \):
\[ \tan(\theta) = \frac{\sqrt{3}}{3} \]

6. **Find the angle \( \theta \):**
The angle whose tangent is \( \frac{\sqrt{3}}{3} \) is \( 30^\circ \):
\[ \theta = 30^\circ \]

### Final Answers:
- **Slope of line AB (m):** \( \frac{\sqrt{3}}{3} \)
- **Inclination of line AB (θ):** \( 30^\circ \)