Find the slope of the line parallel to AB if :
`A = (0, -3) and B = (-2,5)`

Answer

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

### Step 1: Identify the coordinates of points A and B.
- A = (0, -3)
- B = (-2, 5)

### Step 2: Use the formula for the slope of a line.
The slope \( m \) of a line passing through two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is given by the formula:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]

### Step 3: Assign the coordinates to the formula.
Here, we can assign:
- \( (x_1, y_1) = (0, -3) \)
- \( (x_2, y_2) = (-2, 5) \)

### Step 4: Substitute the coordinates into the slope formula.
Now, substituting the values into the formula:
\[ m = \frac{5 - (-3)}{-2 - 0} \]

### Step 5: Simplify the expression.
This simplifies to:
\[ m = \frac{5 + 3}{-2} = \frac{8}{-2} = -4 \]

### Step 6: Determine the slope of the parallel line.
Since parallel lines have the same slope, the slope of the line parallel to AB is also:
\[ m = -4 \]

### Final Answer:
The slope of the line parallel to AB is \(-4\).

---