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The worksheet asks you to determine whether the data sets show direct variation and, if so, to write an equation that describes the relationship. Let's go through each data set:

### 1. Resistance (ohms) and Current (amps)
- **Data Points**: 
  - (4, 2), (5, 2.4), (6, 3), (8, 4), (15, 5)
  
- **Analysis**: To check for direct variation, we need to determine if the ratio of Current (amps) to Resistance (ohms) is constant (i.e., $ \text{Current} = k \times \text{Resistance} $).
  - Ratios: $ \frac{2}{4} = 0.5 $, $ \frac{2.4}{5} = 0.48 $, $ \frac{3}{6} = 0.5 $, $ \frac{4}{8} = 0.5 $, $ \frac{5}{15} = 0.33 $.
  - The ratios are not consistent, so this does **not** show direct variation.

### 2. Dosage (mg) and Weight (lb)
- **Data Points**: 
  - (8, 160), (15, 300), (28, 560), (47, 940)
  
- **Analysis**: Check if the ratio is consistent.
  - Ratios: $ \frac{160}{8} = 20 $, $ \frac{300}{15} = 20 $, $ \frac{560}{28} = 20 $, $ \frac{940}{47} = 20 $.
  - The ratios are constant, showing direct variation with $ k = 20 $.
  - **Equation**: $ \text{Dosage} = 20 \times \text{Weight} $.

### 3. Games and At-bats
- **Data Points**: 
  - (20, 62), (30, 93), (50, 155), (160, 496)
  
- **Analysis**: Check if the ratio is consistent.
  - Ratios: $ \frac{62}{20} = 3.1 $, $ \frac{93}{30} = 3.1 $, $ \frac{155}{50} = 3.1 $, $ \frac{496}{160} = 3.1 $.
  - The ratios are constant, showing direct variation with $ k = 3.1 $.
  - **Equation**: $ \text{At-bats} = 3.1 \times \text{Games} $.

### 4. Price ($) and Sales tax ($)
- **Data Points**: 
  - (4, 0.29), (12, 0.87), (36, 2.61), (60, 4.35)
  
- **Analysis**: Check if the ratio is consistent.
  - Ratios: $ \frac{0.29}{4} = 0.0725 $, $ \frac{0.87}{12} = 0.0725 $, $ \frac{2.61}{36} = 0.0725 $, $ \frac{4.35}{60} = 0.0725 $.
  - The ratios are constant, showing direct variation with $ k = 0.0725 $.
  - **Equation**: $ \text{Sales tax} = 0.0725 \times \text{Price} $.

### Summary:
1. **No direct variation**.
2. Direct variation with equation: $ \text{Dosage} = 20 \times \text{Weight} $.
3. Direct variation with equation: $ \text{At-bats} = 3.1 \times \text{Games} $.
4. Direct variation with equation: $ \text{Sales tax} = 0.0725 \times \text{Price} $.

Would you like any further details or have any questions?

### Additional Questions:
1. How do you determine if a set of data shows inverse variation?
2. What are other ways to identify direct variation besides finding a constant ratio?
3. How can direct variation equations be applied in real-world scenarios?
4. What happens to the graph of a direct variation equation?
5. Can direct variation involve more complex equations than linear ones?

**Tip:** Checking if the ratio between pairs of values remains constant is the key to identifying 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. Explore relationships like Resistance and Current, Dosage and Weight, Games and At-bats, and Price and Sales Tax. Learn how to calculate constant ratios and write direct variation equations.

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