To determine if the ordered pairs represent direct variation or inverse variation, we need to analyze the relationships between the x and y values in the pairs.
Direct Variation
For direct variation, the relationship can be described by the equation \(y = kx\), where \(k\) is a constant. This means that when \(x\) increases, \(y\) also increases proportionally.
Inverse Variation
For inverse variation, the relationship can be described by the equation \(y = \frac{k}{x}\), where \(k\) is a constant. This means that when \(x\) increases, \(y\) decreases in such a way that the product \(xy\) is constant.
Now let's check the ordered pairs:
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For (2, 6):
- Check direct variation: \(6 = k \cdot 2 \Rightarrow k = 3\).
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For (3, 9):
- Check direct variation: \(9 = k \cdot 3 \Rightarrow k = 3\).
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For (5, 15):
- Check direct variation: \(15 = k \cdot 5 \Rightarrow k = 3\).
Since \(k\) is consistent across all pairs and equal to 3, the relationship is a direct variation.
Conclusion
The ordered pairs (2,6), (3,9), and (5,15) represent direct variation.