https://file.aiquickdraw.com/mathbot/file/1725484411747p2n1g5c4.jpg

To find the constant of proportionality in the table provided in the image, we need to determine the ratio between the distance (in meters) and the time (in seconds). The constant of proportionality \( k \) can be calculated using the formula:

\[
k = \frac{\text{Distance (m)}}{\text{Time (s)}}
\]

Let's calculate \( k \) for each pair of values:

- For \( t = 1 \) s, \( d = 6 \) m: 
  \[
  k = \frac{6}{1} = 6
  \]
- For \( t = 2 \) s, \( d = 12 \) m:
  \[
  k = \frac{12}{2} = 6
  \]
- For \( t = 3 \) s, \( d = 18 \) m:
  \[
  k = \frac{18}{3} = 6
  \]
- For \( t = 4 \) s, \( d = 24 \) m:
  \[
  k = \frac{24}{4} = 6
  \]

The constant of proportionality \( k \) is consistent across all the data points and is equal to 6.

**Answer:** The constant of proportionality is 6.

Would you like more details, or do you have any other questions?

### Related Questions:
1. How do you determine if two variables are directly proportional?
2. What are some examples of situations where a constant of proportionality might be used in real life?
3. How can the concept of proportionality be applied to solve problems in physics?
4. What would happen to the graph of this relationship if the constant of proportionality was different?
5. Can you have a proportional relationship with a constant that is not a whole number?

**Tip:** When dealing with proportional relationships, always check that the ratio between the variables remains constant across all data points.

What is the constant of proportionality based on the given table of time and distance?

Learn how to determine the constant of proportionality from a table of time and distance values. The problem involves understanding ratios and linear relationships, with a clear explanation of how to calculate the constant k using the formula k = Distance (m) / Time (s). Suitable for students in Grades 6-8.

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