Question

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

x	y
6	4
9	6
15	10
x	y
4	3
8	6
12	9

Explanation:

Step1: Recall Proportional Relationship

A proportional relationship between \( x \) and \( y \) means \( \frac{y}{x}=k \) (constant) for all pairs \((x,y)\).

Step2: Check Blue Table

For blue table:

• First pair: \( \frac{4}{6}=\frac{2}{3} \)
• Second pair: \( \frac{6}{9}=\frac{2}{3} \)
• Third pair: \( \frac{10}{15}=\frac{2}{3} \)

Constant \( k = \frac{2}{3} \), so proportional.

Step3: Check Green Table

For green table:

• First pair: \( \frac{3}{4} \)
• Second pair: \( \frac{6}{8}=\frac{3}{4} \)
• Third pair: \( \frac{9}{12}=\frac{3}{4} \)

Constant \( k=\frac{3}{4} \), so proportional.

Answer:

Both the blue - colored table (with \( x,y \) values \( (6,4),(9,6),(15,10) \)) and the green - colored table (with \( x,y \) values \( (4,3),(8,6),(12,9) \)) show a proportional relationship between \( x \) and \( y \).