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### Direct Variation Problems

1. **Determine if the data sets show direct variation, and write the equation if so.**

#### Problem 1: Resistance (amps) vs. Current (ohms)
   - Resistance values: \(3, 5, 6, 8\)
   - Current values: \(4, 2.4, 2, 1.5\)

   To check for direct variation, we calculate the ratio of current to resistance for each pair. If all ratios are the same, it's a direct variation:
   \[
   \frac{4}{3} \approx 1.33, \quad \frac{2.4}{5} = 0.48, \quad \frac{2}{6} \approx 0.33, \quad \frac{1.5}{8} \approx 0.19
   \]
   These ratios are not constant, so this does **not** show direct variation.

#### Problem 2: Weight (lb) vs. Dosage (mg)
   - Weight values: \(8, 15, 28, 47\)
   - Dosage values: \(160, 300, 560, 940\)

   Let's check the ratio:
   \[
   \frac{160}{8} = 20, \quad \frac{300}{15} = 20, \quad \frac{560}{28} = 20, \quad \frac{940}{47} = 20
   \]
   Since the ratios are the same, this data shows **direct variation**. The equation is:
   \[
   \text{Dosage} = 20 \times \text{Weight}
   \]

#### Problem 3: Games vs. At-bats
   - Games values: \(20, 30, 50, 160\)
   - At-bats values: \(62, 93, 155, 

Determine whether the data sets show direct variation. If so, write an equation that describes the relationship. Example questions involve Resistance vs. Current, Weight vs. Dosage, Games vs. At-bats, Price vs. Sales tax, and other direct variation problems.

Learn how to determine direct variation and write equations from data sets involving real-world examples like resistance vs. current, weight vs. dosage, and price vs. sales tax. This guide covers direct variation concepts, ratios, and linear relationships suitable for Grades 7-10.

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