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Let's walk through the math problem together.

### 2. A lemonade recipe calls for \( \frac{1}{4} \) cup of lemon juice for every cup of water.

#### Part a: Use the table to answer these questions.
The given table looks like this:

| \(x\) (Cups of Water) | \(y\) (Cups of Lemon Juice) |
|----------------------|-----------------------------|
| 1                    | \( \frac{1}{4} \)           |
| 2                    | \( \frac{1}{2} \)           |
| 3                    | \( \frac{3}{4} \)           |
| 4                    | 1                           |

i. **What does \(x\) represent?**  
   - \(x\) represents the number of cups of **water**.

ii. **What does \(y\) represent?**  
   - \(y\) represents the amount of **lemon juice** needed, measured in cups.

iii. **Is there a proportional relationship between \(x\) and \(y\)?**  
   - Yes, this is a proportional relationship because the ratio between \(y\) and \(x\) is constant.  
     \[
     \frac{y}{x} = \frac{1/4}{1} = \frac{1/2}{2} = \frac{3/4}{3} = \frac{1}{4}
     \]
   The constant ratio of \(\frac{1}{4}\) confirms proportionality.

#### Part b: Plot the pairs in the table on a coordinate plane.
To do this:
1. Plot the points (1, \( \frac{1}{4} \)), (2, \( \frac{1}{2} \)), (3, \( \frac{3}{4} \)), and (4, 1) on the coordinate plane.
2. The graph should form a straight line passing through the origin (0, 0), showing the proportional relationship.

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Do you want to explore the graph in more detail, or have any follow-up questions?  
Here are 5 related questions to deepen your understanding:

1. What would the equation of the proportional relationship be?
2. If 5 cups of water were used, how much lemon juice would be required?
3. How would the graph change if the ratio was \(\frac{1}{2}\) instead of \(\frac{1}{4}\)?
4. Can you think of another real-life example of a proportional relationship?
5. How can you verify proportionality using a table or equation?

**Tip:** In a proportional relationship, the graph always passes through the origin (0, 0). This is a key feature!

A lemonade recipe calls for 1/4 cup of lemon juice for every cup of water. Use the table to answer these questions: (i) What does x represent? (ii) What does y represent? (iii) Is there a proportional relationship between x and y? (b) Plot the pairs in the table in a coordinate plane.

Learn how to analyze a proportional relationship between cups of water and lemon juice in a lemonade recipe. This problem covers key concepts in ratios, proportional relationships, and coordinate graphing, suitable for Grade 7 students.

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