Question

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

x	y
3	13/4
4	5
6	10
x	y
3	1
11	11/3
12	4

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 Green Table

• For \( x = 3, y=\frac{13}{4} \): \( \frac{y}{x}=\frac{\frac{13}{4}}{3}=\frac{13}{12}\approx1.083 \)
• For \( x = 4, y = 5 \): \( \frac{y}{x}=\frac{5}{4}=1.25 \)
• For \( x = 6, y = 10 \): \( \frac{y}{x}=\frac{10}{6}=\frac{5}{3}\approx1.666 \)

Since the ratios are not constant, the green table does not show a proportional relationship.

Step3: Check Purple Table

• For \( x = 3, y = 1 \): \( \frac{y}{x}=\frac{1}{3}\approx0.333 \)
• For \( x = 11, y=\frac{11}{3} \): \( \frac{y}{x}=\frac{\frac{11}{3}}{11}=\frac{1}{3}\approx0.333 \)
• For \( x = 12, y = 4 \): \( \frac{y}{x}=\frac{4}{12}=\frac{1}{3}\approx0.333 \)

The ratio \( \frac{y}{x}=\frac{1}{3} \) is constant, so the purple table shows a proportional relationship.

Answer:

The purple - colored table (the table with \( x \) and \( y \) in purple header)