Question

Determine if the ordered pairs represent a direct variation or inverse variation.

(2,6),(3,9),(5,15)

direct variation

inverse variation

Answer 1

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:

1. **For (2, 6)**:
- Check direct variation: \(6 = k \cdot 2 \Rightarrow k = 3\).

2. **For (3, 9)**:
- Check direct variation: \(9 = k \cdot 3 \Rightarrow k = 3\).

3. **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.