Question

select the tables that show a proportional relationship between x and y.

x	y
4	1
8	2
12	3
x	y
1	2
3	6
4	8

Explanation:

Step1: Check Green Table

For a proportional relationship, \( \frac{y}{x} \) should be constant.
For \( x = 4, y = 1 \): \( \frac{1}{4}=0.25 \)
For \( x = 8, y = 2 \): \( \frac{2}{8}=0.25 \)
For \( x = 12, y = 3 \): \( \frac{3}{12}=0.25 \)
Constant ratio, so green table is proportional.

Step2: Check Orange Table

For \( x = 1, y = 2 \): \( \frac{2}{1}=2 \)
For \( x = 3, y = 6 \): \( \frac{6}{3}=2 \)
For \( x = 4, y = 8 \): \( \frac{8}{4}=2 \)
Constant ratio, so orange table is proportional.

Answer:

Both the green - colored table (with \( x \) values 4, 8, 12 and \( y \) values 1, 2, 3) and the orange - colored table (with \( x \) values 1, 3, 4 and \( y \) values 2, 6, 8) show a proportional relationship between \( x \) and \( y \).