Question

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

x	y
6	8
9	12

x	y
3	7
6	10

Explanation:

Step1: Recall proportional relationship rule

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

Step2: Check first table

For the first table:

• When \( x = 3, y = 4 \), \( \frac{y}{x}=\frac{4}{3} \)
• When \( x = 6, y = 8 \), \( \frac{y}{x}=\frac{8}{6}=\frac{4}{3} \)
• When \( x = 9, y = 12 \), \( \frac{y}{x}=\frac{12}{9}=\frac{4}{3} \)

All ratios are equal (\( k=\frac{4}{3} \)), so it's proportional.

Step3: Check second table

For the second table:

• When \( x = 1, y = 5 \), \( \frac{y}{x}=5 \)
• When \( x = 3, y = 7 \), \( \frac{y}{x}=\frac{7}{3}\approx2.33 \)
• When \( x = 6, y = 10 \), \( \frac{y}{x}=\frac{10}{6}=\frac{5}{3}\approx1.67 \)

Ratios are not equal, so it's not proportional.

Answer:

The first table (with \( x = 3,6,9 \) and \( y = 4,8,12 \)) shows a proportional relationship.