*x* (months)

*y* (pounds)

3

13

4

17

8

33

10

41

According to the values in the table, do *x* and *y* have a proportional relationship?

yes

no

What is the constant of proportionality? Write your answer as a whole number or decimal.

pounds per month

To determine if \( x \) (months) and \( y \) (pounds) have a proportional relationship, we need to check if there is a constant of proportionality \( k \) such that:

\[
y = k \cdot x
\]

for each \( x \) and corresponding \( y \) in the table.

Let's examine each pair and calculate \( k = \frac{y}{x} \) for consistency:

1. For \( x = 3 \) and \( y = 13 \):
   \[
   k = \frac{13}{3} \approx 4.33
   \]

2. For \( x = 4 \) and \( y = 17 \):
   \[
   k = \frac{17}{4} = 4.25
   \]

3. For \( x = 8 \) and \( y = 33 \):
   \[
   k = \frac{33}{8} = 4.125
   \]

4. For \( x = 10 \) and \( y = 41 \):
   \[
   k = \frac{41}{10} = 4.1
   \]

Since the values of \( k \) are not the same across all pairs, \( x \) and \( y \) do not have a proportional relationship. The values of \( k \) change slightly with each pair, indicating that there isn’t a single constant of proportionality.

**Answer:**

- **Proportional relationship:** No
- **Constant of proportionality:** None, as the relationship is not proportional.

Would you like more details or have any questions?

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### Related Questions

1. How do you determine if two variables are proportional from a table of values?
2. Can a relationship be approximately proportional if the values of \( k \) are close?
3. How would you calculate the constant of proportionality if the relationship were proportional?
4. What are examples of situations where a proportional relationship is commonly found?
5. How does a proportional relationship differ from a linear relationship in general?

**Tip:** When values don’t match exactly for \( k = \frac{y}{x} \) across pairs, even slight differences mean the relationship isn't truly proportional.

According to the values in the table, do x and y have a proportional relationship? If so, what is the constant of proportionality?

Explore how to check if x and y values in a table have a proportional relationship and find the constant of proportionality. This problem includes step-by-step calculations to determine if a constant k exists across data pairs, suitable for students in Grades 6-8.

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