Question

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

x	y
3	5
6	10
9	15
x	y
2	3
4	9
6	19

Explanation:

Step1: Check first table

For a proportional relationship, \( \frac{y}{x} \) should be constant.
For \( x = 3, y = 5 \): \( \frac{5}{3} \approx 1.67 \)
For \( x = 6, y = 10 \): \( \frac{10}{6}=\frac{5}{3} \approx 1.67 \)
For \( x = 9, y = 15 \): \( \frac{15}{9}=\frac{5}{3} \approx 1.67 \)
Constant ratio, so proportional.

Step2: Check second table

For \( x = 2, y = 3 \): \( \frac{3}{2}=1.5 \)
For \( x = 4, y = 9 \): \( \frac{9}{4}=2.25 \)
For \( x = 6, y = 19 \): \( \frac{19}{6}\approx 3.17 \)
Ratios not constant, so not proportional.

Answer:

The table on the left (with \( x = 3,6,9 \) and \( y = 5,10,15 \))