Question

select the tables that show a proportional relationship between x and y.
first table (x,y): (2,2), (5,5), (6,6)
second table (x,y): (1,5), (3,9), (7,17)

Explanation:

Step1: Recall Proportional Relationship

A proportional relationship between \( x \) and \( y \) means \( y = kx \) (where \( k \) is a constant), so \( \frac{y}{x} \) should be the same for all pairs of \( x \) and \( y \).

Step2: Check First Table

For the first table:

• When \( x = 2 \), \( y = 2 \), \( \frac{y}{x}=\frac{2}{2} = 1 \)
• When \( x = 5 \), \( y = 5 \), \( \frac{y}{x}=\frac{5}{5}=1 \)
• When \( x = 6 \), \( y = 6 \), \( \frac{y}{x}=\frac{6}{6}=1 \)

All ratios are equal (\( k = 1 \)), so it's proportional.

Step3: Check Second Table

For the second table:

• When \( x = 1 \), \( y = 5 \), \( \frac{y}{x}=\frac{5}{1}=5 \)
• When \( x = 3 \), \( y = 9 \), \( \frac{y}{x}=\frac{9}{3}=3 \)
• When \( x = 7 \), \( y = 17 \), \( \frac{y}{x}=\frac{17}{7}\approx2.43 \)

Ratios are not equal, so it's not proportional.

Answer:

The table on the left (with \( x \) and \( y \) values \( (2,2) \), \( (5,5) \), \( (6,6) \)) shows a proportional relationship.