Question

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

x y
4 2
9 3
16 4x y 4 2 9 3 16 4

x y
2 10
5 20
6 30x y 2 10 5 20 6 30

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

x y
10 2
15 3
40 8


x y 10 2 15 3 40 8
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Answer 1

To determine which table demonstrates a proportional relationship, we need to look for a constant ratio between the values of \(y\) and \(x\). A proportional relationship can be described by the equation \(y = kx\), where \(k\) is a constant.

Let's analyze each table:

1. **Table 1:**
```
x | y
--------
4 | 2 -> 2/4 = 0.5
9 | 3 -> 3/9 = 1/3
16 | 4 -> 4/16 = 1/4
```
The ratios are not constant.

2. **Table 2:**
```
x | y
--------
2 | 10 -> 10/2 = 5
5 | 20 -> 20/5 = 4
6 | 30 -> 30/6 = 5
```
The ratios are not constant.

3. **Table 3:**
```
x | y
--------
8 | 2 -> 2/8 = 1/4
12 | 3 -> 3/12 = 1/4
40 | 4 -> 4/40 = 1/10
```
The ratios are not constant.

4. **Table 4:**
```
x | y
--------
10 | 2 -> 2/10 = 1/5
15 | 3 -> 3/15 = 1/5
40 | 8 -> 8/40 = 1/5
```
All ratios are equal to \(1/5\), so this table demonstrates a proportional relationship.

Therefore, the table that shows a proportional relationship is **Table 4**.