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Let's go through the questions step-by-step.

### Question a: Use the table to answer these questions.

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

#### ii. What does \( y \) represent?
- \( y \) represents the amount of lemon juice (in cups) needed for each corresponding amount of water, based on the given ratio.

#### iii. Is there a proportional relationship between \( x \) and \( y \)?
- Yes, there is a proportional relationship. For every increase of 1 cup of water (\( x \)), the amount of lemon juice (\( y \)) increases by \( \frac{1}{4} \) cup. The ratio of lemon juice to water is constant at \( \frac{y}{x} = \frac{1}{4} \), indicating a proportional relationship.

### Question b: Plot the pairs in the table in a coordinate plane.

The coordinate pairs from the table are:
1. \( (1, \frac{1}{4}) \)
2. \( (2, \frac{1}{2}) \)
3. \( (3, \frac{3}{4}) \)
4. \( (4, 1) \)

You would plot these points on a graph with \( x \) as the horizontal axis (number of cups of water) and \( y \) as the vertical axis (cups of lemon juice). Each point should align along a straight line due to the proportional relationship between \( x \) and \( y \).

Would you like further details or assistance with graphing these points? 

### Follow-up Questions
1. How would the graph change if the recipe called for \( \frac{1}{3} \) cup of lemon juice per cup of water?
2. Can you write an equation that represents the relationship between \( x \) and \( y \)?
3. What would the amount of lemon juice be for 10 cups of water?
4. How would you explain proportional relationships in general?
5. What is the slope of the line representing this relationship, and what does it mean in this context?

### Tip
To confirm a proportional relationship, check if all \( y \)-values are obtained by multiplying the \( x \)-values by a constant factor (the unit rate).

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

Explore the concept of proportional relationships in this lemonade recipe question, which involves plotting a ratio of lemon juice to water on a coordinate plane. Learn about ratios and how to determine if x and y have a proportional relationship. Suitable for middle school students in Grades 6-8.

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