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Let's analyze the table to determine if there is a proportional relationship between \( x \) (number of cans) and \( y \) (cost in dollars).

A proportional relationship occurs when the ratio between \( y \) and \( x \) remains constant. In other words, \( \frac{y}{x} \) should be the same for all pairs of values.

Let's calculate the ratio \( \frac{y}{x} \) for each pair:

1. For \( x = 11 \) and \( y = 24 \), the ratio is \( \frac{24}{11} \approx 2.18 \).
2. For \( x = 36 \) and \( y = 49 \), the ratio is \( \frac{49}{36} \approx 1.36 \).
3. For \( x = 66 \) and \( y = 79 \), the ratio is \( \frac{79}{66} \approx 1.20 \).
4. For \( x = 85 \) and \( y = 98 \), the ratio is \( \frac{98}{85} \approx 1.15 \).

Since the ratios are not equal, \( x \) and \( y \) do not have a proportional relationship.

Would you like more details on proportional relationships, or have any questions about this explanation? Here are five related questions for practice:

1. What does a proportional relationship mean in terms of graphing?
2. How would you find the constant of proportionality if a relationship were proportional?
3. Can you calculate the difference in the cost per can as the number of cans increases?
4. What would the equation of a proportional relationship look like?
5. How can you tell if a relationship is linear but not proportional?

**Tip**: In a proportional relationship, the graph will be a straight line that passes through the origin (0, 0).

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

Learn how to determine if the number of chili cans (x) and the total cost (y) have a proportional relationship by calculating ratios from a table of values. This problem focuses on proportionality, ratios, and basic algebra, suitable for students in Grades 6-8.

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