Question

which table shows a proportional relationship between x and y?
a

x	y
2	3
3	6

b

x	y
2	3
3	5

c

x	y
2	4
3	6

(part of table d is shown but cut off)

Explanation:

Step1: Recall Proportional Relationship

A proportional relationship between \( x \) and \( y \) means \( y = kx \) (where \( k \) is a constant), so \( \frac{y}{x}=k \) for all pairs \((x,y)\) (and \( x
eq0 \)). Also, when \( x = 0 \), \( y \) should be \( 0 \) (though not all tables have \( x = 0 \), the ratio \( \frac{y}{x} \) must be constant).

Step2: Check Option A

For table A:

• When \( x = 1 \), \( y = 0 \), \( \frac{y}{x}=\frac{0}{1}=0 \)
• When \( x = 2 \), \( y = 3 \), \( \frac{y}{x}=\frac{3}{2}=1.5 \)
• Ratios are not equal, so not proportional.

Step3: Check Option B

For table B:

• When \( x = 1 \), \( y = 1 \), \( \frac{y}{x}=1 \)
• When \( x = 2 \), \( y = 3 \), \( \frac{y}{x}=\frac{3}{2}=1.5 \)
• Ratios are not equal, so not proportional.

Step4: Check Option C

For table C:

• When \( x = 1 \), \( y = 2 \), \( \frac{y}{x}=\frac{2}{1}=2 \)
• When \( x = 2 \), \( y = 4 \), \( \frac{y}{x}=\frac{4}{2}=2 \)
• When \( x = 3 \), \( y = 6 \), \( \frac{y}{x}=\frac{6}{3}=2 \)
• Ratios are equal (\( k = 2 \)), so proportional.

Answer:

C. The table with \( x = 1, y = 2 \); \( x = 2, y = 4 \); \( x = 3, y = 6 \)