Question

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

x	y		x	y
12	6		6	2
15	8		12	4

Explanation:

Step1: Recall proportional relationship rule

For a proportional relationship between \( x \) and \( y \), the ratio \( \frac{y}{x} \) (or \( \frac{x}{y} \)) must be constant for all pairs of \( x \) and \( y \).

Step2: Analyze the first table (orange)

• For \( x = 6, y = 2 \): \( \frac{y}{x}=\frac{2}{6}=\frac{1}{3}\approx0.333 \)
• For \( x = 12, y = 6 \): \( \frac{y}{x}=\frac{6}{12}=\frac{1}{2} = 0.5 \)
• For \( x = 15, y = 8 \): \( \frac{y}{x}=\frac{8}{15}\approx0.533 \)

Since the ratios are not constant, the first table does not show a proportional relationship.

Step3: Analyze the second table (green)

• For \( x = 3, y = 1 \): \( \frac{y}{x}=\frac{1}{3}\approx0.333 \)
• For \( x = 6, y = 2 \): \( \frac{y}{x}=\frac{2}{6}=\frac{1}{3}\approx0.333 \)
• For \( x = 12, y = 4 \): \( \frac{y}{x}=\frac{4}{12}=\frac{1}{3}\approx0.333 \)

Since the ratio \( \frac{y}{x}=\frac{1}{3} \) is constant for all pairs, the second table shows a proportional relationship.

Answer:

The table with \( x \) values 3, 6, 12 and \( y \) values 1, 2, 4 (the green - colored table) shows a proportional relationship.