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Let's analyze the worksheet content to solve the problems step-by-step.

### Problem Analysis:

1. **Direct Variation Concept:**
   If two variables $ x $ and $ y $ show direct variation, it means they can be represented by an equation of the form $ y = kx $, where $ k $ is the constant of proportionality.

2. **Worksheet Problems:**
   The worksheet requires determining if the given datasets show direct variation. If they do, we need to find the equation describing the relationship.

### Problem Details:

1. **Problem 1:** 
   - **Resistance (amps)** vs. **Current (ohms)**.
   - Check if $ \frac{\text{Resistance}}{\text{Current}} $ is constant.

2. **Problem 2:** 
   - **Weight (lb)** vs. **Dosage (mg)**.
   - Check if $ \frac{\text{Dosage}}{\text{Weight}} $ is constant.

3. **Problem 3:** 
   - **Games** vs. **At-bats**.
   - Check if $ \frac{\text{At-bats}}{\text{Games}} $ is constant.

4. **Problem 4:** 
   - **Price (\$)** vs. **Sales tax (\$)**.
   - Check if $ \frac{\text{Sales Tax}}{\text{Price}} $ is constant.

5. **Problem 5:**
   - Cups vary directly with tablespoons. Given equation form is $ y = kx $, find $ k $ from the graph and then calculate for 56 tablespoons.

6. **Problem 6:**
   - Calories vary directly with protein grams. Use the graph to find the constant $ k $, then calculate for 25 grams of protein.

### Solving Direct Variation:

Let's go through each problem to identify the constant of proportionality $ k $ and confirm direct variation.

1. **Problem 1:** Check $ k = \frac{\text{Resistance}}{\text{Current}} $.
2. **Problem 2:** Check $ k = \frac{\text{Dosage}}{\text{Weight}} $.
3. **Problem 3:** Check $ k = \frac{\text{At-bats}}{\text{Games}} $.
4. **Problem 4:** Check $ k = \frac{\text{Sales Tax}}{\text{Price}} $.
5. **Problem 5:** Use given graph to find $ k $, then calculate for 56 tablespoons.
6. **Problem 6:** Use graph to find $ k $, then calculate for 25 grams of protein.

Would you like detailed solutions for each problem, or is there a specific problem you'd like to focus on first? 

### Relative Questions:

1. How can you determine if two variables show direct variation?
2. What is the role of the constant of proportionality in direct variation?
3. How do you use a graph to find the constant of proportionality?
4. Can direct variation be applied to non-linear relationships?
5. How would you solve for unknown values using a direct variation equation?

### Tip:
Always check if the ratio $ \frac{y}{x} $ remains constant across all data points to confirm direct variation.

Determine whether the data sets show direct variation. If so, write an equation that describes the relationship.

Analyze data sets to determine if they show direct variation. Learn how to write equations that describe the relationship and find the constant of proportionality using examples such as resistance vs. current, weight vs. dosage, and more. Suitable for students in Grades 8-10.

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