Question

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

x | y
1 | 5/2
3 | 15/2
8 | 20

x | y
3 | 9/2
5 | 15/2
10 | 15

Explanation:

Step1: Recall Proportional Relationship

A proportional relationship between \( x \) and \( y \) means \( y = kx \) (or \( \frac{y}{x}=k \), where \( k \) is a constant). So we check \( \frac{y}{x} \) for each pair in the tables.

Step2: Check First Table

• For \( x = 1 \), \( y=\frac{5}{2} \): \( \frac{y}{x}=\frac{\frac{5}{2}}{1}=\frac{5}{2} \)
• For \( x = 3 \), \( y=\frac{15}{2} \): \( \frac{y}{x}=\frac{\frac{15}{2}}{3}=\frac{15}{2}\times\frac{1}{3}=\frac{5}{2} \)
• For \( x = 8 \), \( y = 20 \): \( \frac{y}{x}=\frac{20}{8}=\frac{5}{2} \)

All ratios are \( \frac{5}{2} \), so first table is proportional.

Step3: Check Second Table

• For \( x = 3 \), \( y=\frac{9}{2} \): \( \frac{y}{x}=\frac{\frac{9}{2}}{3}=\frac{9}{2}\times\frac{1}{3}=\frac{3}{2} \)
• For \( x = 5 \), \( y=\frac{15}{2} \): \( \frac{y}{x}=\frac{\frac{15}{2}}{5}=\frac{15}{2}\times\frac{1}{5}=\frac{3}{2} \)
• For \( x = 10 \), \( y = 15 \): \( \frac{y}{x}=\frac{15}{10}=\frac{3}{2} \)

All ratios are \( \frac{3}{2} \), so second table is proportional.

Answer:

Both tables (the left table with \( x = 1, 3, 8 \) and the right table with \( x = 3, 5, 10 \)) show a proportional relationship.