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To determine whether the relationship between the number of empanadas and their price is proportional, we need to check if the ratio of empanadas to price is constant.

### Table Data:
- 2 empanadas cost 1 dollar
- 4 empanadas cost 2 dollars
- 6 empanadas cost 3 dollars
- 8 empanadas cost 4 dollars

### Step 1: Check if the relationship is proportional
A relationship is proportional if the ratio between two quantities is constant. In this case, we check the price per empanada for each entry:

- Price per empanada = $\frac{\text{Price}}{\text{Number of empanadas}}$

For 2 empanadas:
\[
\frac{1 \text{ dollar}}{2 \text{ empanadas}} = 0.5 \text{ dollars per empanada}
\]

For 4 empanadas:
\[
\frac{2 \text{ dollars}}{4 \text{ empanadas}} = 0.5 \text{ dollars per empanada}
\]

For 6 empanadas:
\[
\frac{3 \text{ dollars}}{6 \text{ empanadas}} = 0.5 \text{ dollars per empanada}
\]

For 8 empanadas:
\[
\frac{4 \text{ dollars}}{8 \text{ empanadas}} = 0.5 \text{ dollars per empanada}
\]

Since the price per empanada is constant at 0.5 dollars, the relationship is proportional.

### Step 2: Find the constant of proportionality
The constant of proportionality is the price per empanada, which is:
\[
k = 0.5 \text{ dollars per empanada}
\]

### Final Answers:
- The price per empanada is **0.5 dollars**.
- The relationship is **proportional**.
- The constant of proportionality is **0.5**.

Let me know if you want further details!

Here are 5 related questions to expand on this:
1. How do we calculate the price for 10 empanadas using the proportional relationship?
2. What if the price per empanada changes to $0.6? How would that affect the proportionality?
3. How do you graph a proportional relationship between price and quantity?
4. What is the importance of the constant of proportionality in real-world problems?
5. How can we use unit rates to compare different pricing strategies?

**Tip:** Whenever you're working with proportional relationships, always check if the ratio stays constant for all data points.

Is the relationship between the price and number of empanadas proportional?

Learn how to determine if the relationship between the number of empanadas and their price is proportional using the unit rate method. This problem covers concepts of proportionality and constant of proportionality, suitable for students in Grades 6-8.

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