Question

Identify the table that demonstrates a proportional relationship.(1 point)
Responses

x y
10 2
15 3
40 8


x y 10 2 15 3 40 8

x y
8 2
12 3
40 4
x y 8 2 12 3 40 4

x y
4 2
9 3
16 4
x y 4 2 9 3 16 4

x y
2 10
5 20
6 30

Answer 1

To determine which table demonstrates a proportional relationship, we need to check if the ratio \( \frac{y}{x} \) is constant for all pairs of \( (x, y) \).

1. **Table 1:**
- \( \frac{2}{10} = 0.2 \)
- \( \frac{3}{15} = 0.2 \)
- \( \frac{8}{40} = 0.2 \)
- **Constant ratio: 0.2**

2. **Table 2:**
- \( \frac{2}{8} = 0.25 \)
- \( \frac{3}{12} = 0.25 \)
- \( \frac{4}{40} = 0.1 \)
- **Not a constant ratio.**

3. **Table 3:**
- \( \frac{2}{4} = 0.5 \)
- \( \frac{3}{9} = \frac{1}{3} \approx 0.333 \)
- \( \frac{4}{16} = 0.25 \)
- **Not a constant ratio.**

4. **Table 4:**
- \( \frac{10}{2} = 5 \)
- \( \frac{20}{5} = 4 \)
- \( \frac{30}{6} = 5 \)
- **Not a constant ratio.**

The only table that demonstrates a proportional relationship is **Table 1**, where the ratio \( \frac{y}{x} \) is constant at 0.2.