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

Question

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.