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To solve the problem, we need to determine which line has a proportionality constant (slope) of 5. This constant is represented as the slope in the equation of the form \( y = mx \), where \( m \) is the constant of proportionality (slope).

### Steps:
1. **Identify points on each line**:
   - Line **A** passes through points like (1, 2) and (2, 6).
   - Line **B** passes through points like (1, 3) and (2, 6).
   - Line **C** passes through points like (1, 1) and (2, 2).

2. **Calculate the slope for each line**:
   - Slope \( m \) is calculated using the formula:
     \[
     m = \frac{y_2 - y_1}{x_2 - x_1}
     \]

   - **For Line A**: 
     Using points (1, 2) and (2, 6):
     \[
     m_A = \frac{6 - 2}{2 - 1} = \frac{4}{1} = 4
     \]

   - **For Line B**: 
     Using points (1, 3) and (2, 6):
     \[
     m_B = \frac{6 - 3}{2 - 1} = \frac{3}{1} = 3
     \]

   - **For Line C**: 
     Using points (1, 1) and (2, 2):
     \[
     m_C = \frac{2 - 1}{2 - 1} = \frac{1}{1} = 1
     \]

3. **Check for the slope of 5**:
   None of the calculated slopes match 5 exactly. However, based on the setup, the question may imply testing other integer points on each line more carefully or interpreting relative options better.

Given the information provided, none of the lines exactly match the slope of 5, which might imply that further investigation is needed if rounding or graph interpretations are involved.

Would you like further details or have other related questions?

### Related questions:
1. How can we interpret proportional relationships in graphs more generally?
2. Can we compute slopes for nonlinear graphs?
3. How do real-life situations use proportionality constants?
4. How do we graph multiple linear equations effectively?
5. What is the significance of slope in physical contexts like speed?

**Tip:** Always use exact points on the graph when calculating slopes, and make sure they align perfectly with the grid.

¿Cuál recta tiene una constante de proporcionalidad de 5 entre y y x?

Learn how to calculate the constant of proportionality between y and x by analyzing lines on a graph. The problem focuses on determining the line with a slope of 5 using the slope formula and understanding proportional relationships. Suitable for students in Grades 6-8.

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