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The worksheet appears to focus on finding the constant of proportionality from various situations and representing this information through tables and graphs.

Let's break down each section:

### 1. Apple Pie Problem
- **Emily's Table**: Relating pies to apples used.
  - The constant of proportionality (k) is the number of apples per pie. You can find \( k \) by dividing apples by pies for each entry in the table.
  
  **Completed Example:**
  - \( k = \frac{20}{4} = 5 \) apples per pie.

  The equation of the line would be \( y = 5x \), where \( y \) is the number of apples, and \( x \) is the number of pies.

### 2. Car Rental Cost Problem
- **Oscar's Table**: Relating miles driven to cost.
  - The constant of proportionality is the cost per mile. You can calculate it as \( k = \frac{\text{Cost}}{\text{Miles}} \).

  **Completed Example:**
  - \( k = \frac{210}{30} = 7 \) dollars per mile.

  The equation would be \( y = 7x \), where \( y \) is the cost, and \( x \) is the number of miles driven.

### 3. Calories Burned Problem
- **David's Table**: Relating minutes of running to calories burned.
  - The constant of proportionality is calories burned per minute. To calculate it, divide the number of calories by the number of minutes.

  **Completed Example:**
  - \( k = \frac{4}{1} = 4 \) calories per minute.

  The equation would be \( y = 4x \), where \( y \) is the calories, and \( x \) is the number of minutes.

### 4. Hourly Earnings Problem
- **Natalia's Table**: Relating hours worked to earnings.
  - The constant of proportionality is the earnings per hour. You can find \( k \) by dividing earnings by hours worked.

  **Completed Example:**
  - \( k = \frac{24}{2} = 12 \) dollars per hour.

  The equation would be \( y = 12x \), where \( y \) is the earnings, and \( x \) is the number of hours worked.

Would you like a detailed breakdown of a specific section or further explanations on graphing and the equations? 

Here are five follow-up questions that you might find useful:
1. How do you find the unit rate from a given table?
2. What is the significance of the constant of proportionality in real-world situations?
3. How can you interpret the equation of the line \( y = kx \) in practical terms?
4. What is the relationship between the slope of the graph and the constant of proportionality?
5. How can you graph proportional relationships if the constant of proportionality is a fraction?

**Tip:** When graphing, always check if the relationship is linear (straight line) to confirm it's proportional.

Worksheet with proportional relationships involving pies, car rental costs, calories burned, and hourly earnings.

This worksheet focuses on finding the constant of proportionality through different scenarios: pies to apples, car rental cost, calories burned, and hourly earnings. It teaches how to use tables, graphs, and the equation y = kx to model proportional relationships.

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