Write down the slopes of the lines
joining L(-p, q) and M(r, s)

Answer

To find the slope of the line joining the points L(-p, q) and M(r, s), we will use the formula for the slope between two points.

### Step-by-Step Solution:

1. **Identify the coordinates of the points:**
- Point L has coordinates (-p, q).
- Point M has coordinates (r, s).

2. **Recall the formula for the slope (m) of a line joining two points (x1, y1) and (x2, y2):**
\[ m = \frac{y2 - y1}{x2 - x1} \]
Here, (x1, y1) = (-p, q) and (x2, y2) = (r, s).

3. **Substitute the coordinates into the slope formula:**
- Let \( x1 = -p \), \( y1 = q \), \( x2 = r \), and \( y2 = s \).
\[ m = \frac{s - q}{r - (-p)} \]

4. **Simplify the denominator:**
\[ m = \frac{s - q}{r + p} \]

5. **Final expression for the slope:**
The slope of the line joining points L and M is:
\[ m = \frac{s - q}{r + p} \]

### Final Answer:
The slope of the line joining points L(-p, q) and M(r, s) is \( \frac{s - q}{r + p} \).

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