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

Question

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

x y
10 2
15 3
40 8

Answer 1

To identify which table demonstrates a proportional relationship, we need to check if the ratio of \(y\) to \(x\) is constant for each pair of \(x\) and \(y\).

1. First Table:

   • (4, 2) → \( \frac{2}{4} = 0.5 \)
   • (9, 3) → \( \frac{3}{9} = \frac{1}{3} \)
   • (16, 4) → \( \frac{4}{16} = 0.25 \)
   • Not proportional.

2. Second Table:

   • (2, 10) → \( \frac{10}{2} = 5 \)
   • (5, 20) → \( \frac{20}{5} = 4 \)
   • (6, 30) → \( \frac{30}{6} = 5 \)
   • Not proportional.

3. Third Table:

   • (8, 2) → \( \frac{2}{8} = 0.25 \)
   • (12, 3) → \( \frac{3}{12} = 0.25 \)
   • (40, 4) → \( \frac{4}{40} = 0.1 \)
   • Not proportional.

4. Fourth Table:

   • (10, 2) → \( \frac{2}{10} = 0.2 \)
   • (15, 3) → \( \frac{3}{15} = 0.2 \)
   • (40, 8) → \( \frac{8}{40} = 0.2 \)
   • Proportional.

The fourth table demonstrates a proportional relationship with a constant ratio of \( \frac{y}{x} = 0.2\).