Question

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

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

x y
8 2
12 3
40 4

Answer 1

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

1. For the first table:
\[
\frac{y}{x} = \frac{2}{4} = 0.5, \quad \frac{3}{9} \approx 0.33, \quad \frac{4}{16} = 0.25
\]
The ratios are not constant.

2. For the second table:
\[
\frac{y}{x} = \frac{10}{2} = 5, \quad \frac{20}{5} = 4, \quad \frac{30}{6} = 5
\]
The ratios are not constant.

3. For the third table:
\[
\frac{y}{x} = \frac{2}{10} = 0.2, \quad \frac{3}{15} = 0.2, \quad \frac{8}{40} = 0.2
\]
The ratios are constant and equal to 0.2.

4. For the fourth table:
\[
\frac{y}{x} = \frac{2}{8} = 0.25, \quad \frac{3}{12} = 0.25, \quad \frac{4}{40} = 0.1
\]
The ratios are not constant.

**Conclusion:** The third table (\( x,y \): 10,2; 15,3; 40,8) demonstrates a proportional relationship with a constant ratio of \( 0.2 \).