Find the value(s) of k so that PQ will be parallel to RS. Given :
`P(2, 4), Q(3, 6), R(8, 1) and S(10, k)`

Answer

To find the value(s) of \( k \) such that line segment \( PQ \) is parallel to line segment \( RS \), we need to ensure that the slopes of both lines are equal.

### Step-by-Step Solution:

1. **Identify the Points**:
- Given points are \( P(2, 4) \), \( Q(3, 6) \), \( R(8, 1) \), and \( S(10, k) \).

2. **Calculate the Slope of Line \( PQ \)**:
- The formula for the slope \( m \) between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
- For points \( P(2, 4) \) and \( Q(3, 6) \):
\[ m_{PQ} = \frac{6 - 4}{3 - 2} = \frac{2}{1} = 2 \]

3. **Calculate the Slope of Line \( RS \)**:
- For points \( R(8, 1) \) and \( S(10, k) \):
\[ m_{RS} = \frac{k - 1}{10 - 8} = \frac{k - 1}{2} \]

4. **Set the Slopes Equal**:
- Since \( PQ \) is parallel to \( RS \), we set their slopes equal:
\[ m_{PQ} = m_{RS} \]
\[ 2 = \frac{k - 1}{2} \]

5. **Solve for \( k \)**:
- Multiply both sides by 2 to eliminate the fraction:
\[ 4 = k - 1 \]
- Add 1 to both sides:
\[ k = 5 \]

### Final Answer:
The value of \( k \) such that line segment \( PQ \) is parallel to line segment \( RS \) is \( k = 5 \).

---