Find the slope of the line passing through the following pairs of points :
`(a, -b)` and `(b, -a)`

Answer

To find the slope of the line passing through the points \((a, -b)\) and \((b, -a)\), we can follow these steps:

### Step 1: Identify the points
The two points given are:
- Point 1: \((x_1, y_1) = (a, -b)\)
- Point 2: \((x_2, y_2) = (b, -a)\)

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

### Step 3: Substitute the values into the formula
Substituting the coordinates of the points into the slope formula:
\[ m = \frac{-a - (-b)}{b - a} \]
This simplifies to:
\[ m = \frac{-a + b}{b - a} \]

### Step 4: Simplify the expression
Rearranging the numerator:
\[ m = \frac{b - a}{b - a} \]

### Step 5: Calculate the slope
Since the numerator and denominator are the same (assuming \(b \neq a\)), we have:
\[ m = 1 \]

### Final Answer
The slope of the line passing through the points \((a, -b)\) and \((b, -a)\) is:
\[ \boxed{1} \]