Question

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

x	y
2	\\(\frac{5}{2}\\)
4	5
12	15
x	y
1	\\(\frac{1}{4}\\)
4	4
6	9

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 (Blue Header)

• For \( x = 2, y=\frac{5}{2} \): \( \frac{y}{x}=\frac{\frac{5}{2}}{2}=\frac{5}{4} \)
• For \( x = 4, y = 5 \): \( \frac{y}{x}=\frac{5}{4} \)
• For \( x = 12, y = 15 \): \( \frac{y}{x}=\frac{15}{12}=\frac{5}{4} \)

All ratios are \( \frac{5}{4} \), so this table is proportional.

Step3: Check Second Table (Purple Header)

• For \( x = 1, y=\frac{1}{4} \): \( \frac{y}{x}=\frac{1}{4} \)
• For \( x = 4, y = 4 \): \( \frac{y}{x}=\frac{4}{4}=1 \) (not equal to \( \frac{1}{4} \))
• For \( x = 6, y = 9 \): \( \frac{y}{x}=\frac{9}{6}=\frac{3}{2} \) (not equal to \( \frac{1}{4} \))

Ratios are not constant, so this table is not proportional.

Answer:

The table with the blue header (containing \( x = 2, y=\frac{5}{2} \); \( x = 4, y = 5 \); \( x = 12, y = 15 \)) shows a proportional relationship.