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
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.