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

Answer 1

A proportional relationship means that the ratio of \( y \) to \( x \) remains constant across all values.

Let's check each option:

1. First Table: \[ \begin{align*} x & : y \ 4 & : 2 \quad (y/x = 2/4 = 0.5) \ 9 & : 3 \quad (y/x = 3/9 = 0.333...) \ 16 & : 4 \quad (y/x = 4/16 = 0.25) \end{align*} \] The ratios are not constant.

2. Second Table: \[ \begin{align*} x & : y \ 8 & : 2 \quad (y/x = 2/8 = 0.25) \ 12 & : 3 \quad (y/x = 3/12 = 0.25) \ 40 & : 4 \quad (y/x = 4/40 = 0.1) \end{align*} \] The ratios are not constant.

3. Third Table: \[ \begin{align*} x & : y \ 2 & : 10 \quad (y/x = 10/2 = 5) \ 5 & : 20 \quad (y/x = 20/5 = 4) \ 6 & : 30 \quad (y/x = 30/6 = 5) \end{align*} \] The ratios are not consistent.

4. Fourth Table: \[ \begin{align*} x & : y \ 10 & : 2 \quad (y/x = 2/10 = 0.2) \ 15 & : 3 \quad (y/x = 3/15 = 0.2) \ 40 & : 8 \quad (y/x = 8/40 = 0.2) \end{align*} \] The ratios are consistent at 0.2.

Thus, the fourth table demonstrates a proportional relationship.