Write down the slopes of the lines
joining P(1, 1) and Q(2, 3)

Answer

To find the slope of the line joining the points P(1, 1) and Q(2, 3), we can use the formula for the slope (m) of a line that passes through two points \((x_1, y_1)\) and \((x_2, y_2)\):

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

### Step-by-Step Solution:

1. **Identify the Coordinates**:
- Let \(P(1, 1)\) be \((x_1, y_1)\) where \(x_1 = 1\) and \(y_1 = 1\).
- Let \(Q(2, 3)\) be \((x_2, y_2)\) where \(x_2 = 2\) and \(y_2 = 3\).

2. **Substitute the Coordinates into the Slope Formula**:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{3 - 1}{2 - 1} \]

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

4. **Substitute the Differences Back into the Formula**:
\[ m = \frac{2}{1} \]

5. **Simplify the Slope**:
\[ m = 2 \]

### Final Answer:
The slope of the line joining the points P(1, 1) and Q(2, 3) is \(2\).