Question

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

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
x y 2 10 5 20 6 30

x y
10 2
15 3
40 8


x y 10 2 15 3 40 8
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Answer 1

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

1. **First table:**
- \( \frac{y}{x} \):
- \( \frac{2}{8} = \frac{1}{4} \)
- \( \frac{3}{12} = \frac{1}{4} \)
- \( \frac{4}{40} = \frac{1}{10} \) (not constant)
- This table does not represent a proportional relationship.

2. **Second table:**
- \( \frac{y}{x} \):
- \( \frac{2}{4} = \frac{1}{2} \)
- \( \frac{3}{9} = \frac{1}{3} \) (not constant)
- \( \frac{4}{16} = \frac{1}{4} \) (not constant)
- This table does not represent a proportional relationship.

3. **Third table:**
- \( \frac{y}{x} \):
- \( \frac{10}{2} = 5 \)
- \( \frac{20}{5} = 4 \) (not constant)
- \( \frac{30}{6} = 5 \) (not constant)
- This table does not represent a proportional relationship.

4. **Fourth table:**
- \( \frac{y}{x} \):
- \( \frac{2}{10} = \frac{1}{5} \)
- \( \frac{3}{15} = \frac{1}{5} \)
- \( \frac{8}{40} = \frac{1}{5} \) (constant)
- This table represents a proportional relationship.

The fourth table demonstrates a proportional relationship.