Find the slope and the inclination of the line AB if :
`A = (-3, -2) and B = (1, 2)`.

Answer

To find the slope and the inclination of the line AB given points A = (-3, -2) and B = (1, 2), we can follow these steps:

### Step 1: Identify the coordinates
We have two points:
- Point A (x₁, y₁) = (-3, -2)
- Point B (x₂, y₂) = (1, 2)

### Step 2: Use the slope formula
The formula for the slope (m) of a line passing through two points (x₁, y₁) and (x₂, y₂) is given by:

\[ m = \frac{y₂ - y₁}{x₂ - x₁} \]

### Step 3: Substitute the values into the formula
Substituting the coordinates of points A and B into the slope formula:

\[ m = \frac{2 - (-2)}{1 - (-3)} \]

### Step 4: Simplify the expression
Calculating the numerator and the denominator:

\[ m = \frac{2 + 2}{1 + 3} = \frac{4}{4} \]

### Step 5: Calculate the slope
Now, simplifying the fraction:

\[ m = 1 \]

So, the slope of the line AB is **1**.

### Step 6: Find the angle of inclination
The angle of inclination (θ) can be found using the relation:

\[ \tan(θ) = m \]

Since we have found that the slope m = 1, we can write:

\[ \tan(θ) = 1 \]

### Step 7: Determine the angle
The angle whose tangent is 1 is:

\[ θ = 45^\circ \]

Thus, the angle of inclination of the line AB is **45 degrees**.

### Final Answer:
- Slope of line AB: **1**
- Angle of inclination: **45 degrees**