The co-ordinates of two points P and Q are (2, 6) and (-3, 5) respectively. Find :
the gradient of PQ. 

Answer

To find the gradient (slope) of the line segment connecting the points P(2, 6) and Q(-3, 5), we can use the formula for the gradient (m) given by:

\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]

### Step-by-Step Solution:

1. **Identify the Coordinates:**
- Point P has coordinates \( (x_1, y_1) = (2, 6) \)
- Point Q has coordinates \( (x_2, y_2) = (-3, 5) \)

2. **Substitute the Coordinates into the Gradient Formula:**
- Using the formula \( m = \frac{y_2 - y_1}{x_2 - x_1} \)
- Substitute \( y_2 = 5 \), \( y_1 = 6 \), \( x_2 = -3 \), and \( x_1 = 2 \):
\[ m = \frac{5 - 6}{-3 - 2} \]

3. **Calculate the Differences:**
- Calculate \( y_2 - y_1 \):
\[ 5 - 6 = -1 \]
- Calculate \( x_2 - x_1 \):
\[ -3 - 2 = -5 \]

4. **Substitute the Differences into the Formula:**
\[ m = \frac{-1}{-5} \]

5. **Simplify the Expression:**
- The negatives cancel out:
\[ m = \frac{1}{5} \]

### Final Answer:
The gradient of the line segment PQ is \( \frac{1}{5} \).

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