Question

Which representation shows a proportional relationship between xx and yy?
A
xx yy
99 33
1515 55
1818 1616
2424 2020
B
x
y
C
xx yy
44 55
1212 1313
1414 1515
2020 2121
D
x
y
Answer
Multiple Choice Answers
AA
BB
CC
DD

Answer 1

To determine which representation shows a proportional relationship between \( x \) and \( y \), we need to check if the ratio \( \frac{y}{x} \) is constant across all given pairs.

For each option:

### Option A:
- \( (99, 33) \): \( \frac{33}{99} = \frac{1}{3} \)
- \( (1515, 55) \): \( \frac{55}{1515} \approx 0.0363 \)
- \( (1818, 1616) \): \( \frac{1616}{1818} \approx 0.888 \)
- \( (2424, 2020) \): \( \frac{2020}{2424} \approx 0.833 \)

The ratios are not constant, so **Option A is not proportional**.

### Option B:
This option does not provide any numerical pairs, so we cannot assess it.

### Option C:
- \( (44, 55) \): \( \frac{55}{44} \approx 1.25 \)
- \( (1212, 1313) \): \( \frac{1313}{1212} \approx 1.083 \)
- \( (1414, 1515) \): \( \frac{1515}{1414} \approx 1.071 \)
- \( (2020, 2121) \): \( \frac{2121}{2020} \approx 1.050 \)

The ratios are not constant, so **Option C is not proportional**.

### Option D:
This option does not provide numerical pairs, so we cannot assess it.

Based on the analysis above, **the only option with pairs is Option A and Option C, both of which are not proportional**. Options B and D lack numerical pairs.

Since neither A nor C shows a proportional relationship and we have no data from B and D, we cannot conclusively identify a correct answer from the options provided. If there are specific values for B and D that need to be analyzed, please provide them for further evaluation.