Question

select the tables that show a proportional relationship between x and y.
first table:
x | y
1 | 3
3 | 7
6 | 13
second table:
x | y
5 | 2
10 | 4
15 | 6

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 first table:

• When \( x = 1, y = 3 \), \( \frac{y}{x}=\frac{3}{1}=3 \)
• When \( x = 3, y = 7 \), \( \frac{y}{x}=\frac{7}{3}\approx2.33

eq3 \)
So first table is not proportional.

Step3: Check second table

For second table:

• When \( x = 5, y = 2 \), \( \frac{y}{x}=\frac{2}{5}=0.4 \)
• When \( x = 10, y = 4 \), \( \frac{y}{x}=\frac{4}{10}=0.4 \)
• When \( x = 15, y = 6 \), \( \frac{y}{x}=\frac{6}{15}=0.4 \)

All ratios are equal (\( k = 0.4 \)), so second table is proportional.

Answer:

The table on the right (with \( x = 5,y = 2 \); \( x = 10,y = 4 \); \( x = 15,y = 6 \)) shows a proportional relationship.