Which representation shows a proportional relationship between xx and yy?

Question

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.