Question

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

x	y
5	4
10	8
15	12

x	y
2	6
3	9
6	18

Explanation:

Step1: Recall Proportional Relationship

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

Step2: Check Green Table

For the green table:

• When \( x = 5 \), \( y = 4 \), so \( \frac{y}{x}=\frac{4}{5}=0.8 \)
• When \( x = 10 \), \( y = 8 \), so \( \frac{y}{x}=\frac{8}{10}=0.8 \)
• When \( x = 15 \), \( y = 12 \), so \( \frac{y}{x}=\frac{12}{15}=0.8 \)

The ratio \( \frac{y}{x} \) is constant (\( 0.8 \)), so it's proportional.

Step3: Check Orange Table

For the orange table:

• When \( x = 2 \), \( y = 6 \), so \( \frac{y}{x}=\frac{6}{2}=3 \)
• When \( x = 3 \), \( y = 9 \), so \( \frac{y}{x}=\frac{9}{3}=3 \)
• When \( x = 6 \), \( y = 18 \), so \( \frac{y}{x}=\frac{18}{6}=3 \)

The ratio \( \frac{y}{x} \) is constant (\( 3 \)), so it's proportional.

Answer:

Both the green - colored table (with \( x,y \) values \( (5,4),(10,8),(15,12) \)) and the orange - colored table (with \( x,y \) values \( (2,6),(3,9),(6,18) \)) show a proportional relationship between \( x \) and \( y \).