Subjects algebra

Direct Variation 7C843D

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1. **Stating the problem:** We need to identify which situation is NOT a direct variation. 2. **Understanding direct variation:** Direct variation means two quantities are related by the formula $$y = kx$$ where $$k$$ is a constant. This means if one quantity doubles, the other doubles as well, and the graph is a straight line through the origin. 3. **Analyzing each option:** - a) Total pay for hours labor: Pay usually equals hourly rate times hours worked, so $$\text{pay} = k \times \text{hours}$$, a direct variation. - b) Cost of apples by the pound: Cost equals price per pound times pounds, so $$\text{cost} = k \times \text{pounds}$$, a direct variation. - c) Cost of a pizza plus a 5 delivery fee: Cost equals price of pizza plus a fixed 5, so $$\text{cost} = k \times \text{pizza price} + 5$$, which is NOT direct variation because of the added constant. - d) Distance a car travels at constant speed: Distance equals speed times time, so $$\text{distance} = k \times \text{time}$$, a direct variation. 4. **Conclusion:** The situation that is NOT direct variation is option c. **Final answer:** c) Cost of a pizza plus a 5 delivery fee