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Which of the following tables represents a proportional relationship?

A.
x 4 6 8 10
y 6 9 12 15

B.
x 1 4 7 10
y 0 3 6 9

C.
x 2 4 6 8
y 3 4 5 6

D.
x 2 3 4 5
y 3 6 9 12

5 answers

To determine which of the given tables represents a proportional relationship, we need to check if the ratio of \(y\) to \(x\) (i.e., \( \frac{y}{x} \)) is constant for all pairs in each table.

Let's analyze each option:

A. \[ \begin{array}{c|c} x & y \ \hline 4 & 6 \quad \frac{6}{4} = 1.5 \ 6 & 9 \quad \frac{9}{6} = 1.5 \ 8 & 12 \quad \frac{12}{8} = 1.5 \ 10 & 15 \quad \frac{15}{10} = 1.5 \ \end{array} \] The ratio \( \frac{y}{x} = 1.5 \) is constant in this table.

B. \[ \begin{array}{c|c} x & y \ \hline 1 & 0 \quad \frac{0}{1} = 0 \ 4 & 3 \quad \frac{3}{4} = 0.75 \ 7 & 6 \quad \frac{6}{7} \approx 0.857 \ 10 & 9 \quad \frac{9}{10} = 0.9 \ \end{array} \] The ratios are not constant.

C. \[ \begin{array}{c|c} x & y \ \hline 2 & 3 \quad \frac{3}{2} = 1.5 \ 4 & 4 \quad \frac{4}{4} = 1 \ 6 & 5 \quad \frac{5}{6} \approx 0.833 \ 8 & 6 \quad \frac{6}{8} = 0.75 \ \end{array} \] The ratios are not constant.

D. \[ \begin{array}{c|c} x & y \ \hline 2 & 3 \quad \frac{3}{2} = 1.5 \ 3 & 6 \quad \frac{6}{3} = 2 \ 4 & 9 \quad \frac{9}{4} = 2.25 \ 5 & 12 \quad \frac{12}{5} = 2.4 \ \end{array} \] The ratios are not constant.

The only table that represents a proportional relationship is Option A:

\[ \begin{array}{c|c} x & y \ \hline 4 & 6 \ 6 & 9 \ 8 & 12 \ 10 & 15 \ \end{array} \]

Thus, A is the answer.

wtf is **

the answers are A B C or D

I apologize for the confusion in my formatting. Let's analyze the options clearly to find which table represents a proportional relationship, focusing specifically on options A, B, C, and D.

For a relationship to be proportional, the ratio \(\frac{y}{x}\) must remain constant for all pairs in the table.

Checking each option:

A. \[ \begin{array}{c|c} x & y \ \hline 4 & 6 \quad \Rightarrow \frac{6}{4} = 1.5 \ 6 & 9 \quad \Rightarrow \frac{9}{6} = 1.5 \ 8 & 12 \quad \Rightarrow \frac{12}{8} = 1.5 \ 10 & 15 \quad \Rightarrow \frac{15}{10} = 1.5 \ \end{array} \]

  • The ratio is constant at 1.5.
    This is a proportional relationship.

B. \[ \begin{array}{c|c} x & y \ \hline 1 & 0 \quad \Rightarrow \frac{0}{1} = 0 \ 4 & 3 \quad \Rightarrow \frac{3}{4} = 0.75 \ 7 & 6 \quad \Rightarrow \frac{6}{7} \approx 0.857 \ 10 & 9 \quad \Rightarrow \frac{9}{10} = 0.9 \ \end{array} \]

  • The ratios are not constant.
    This is not a proportional relationship.

C. \[ \begin{array}{c|c} x & y \ \hline 2 & 3 \quad \Rightarrow \frac{3}{2} = 1.5 \ 4 & 4 \quad \Rightarrow \frac{4}{4} = 1 \ 6 & 5 \quad \Rightarrow \frac{5}{6} \approx 0.833 \ 8 & 6 \quad \Rightarrow \frac{6}{8} = 0.75 \ \end{array} \]

  • The ratios are not constant.
    This is not a proportional relationship.

D. \[ \begin{array}{c|c} x & y \ \hline 2 & 3 \quad \Rightarrow \frac{3}{2} = 1.5 \ 3 & 6 \quad \Rightarrow \frac{6}{3} = 2 \ 4 & 9 \quad \Rightarrow \frac{9}{4} = 2.25 \ 5 & 12 \quad \Rightarrow \frac{12}{5} = 2.4 \ \end{array} \]

  • The ratios are not constant.
    This is not a proportional relationship.

Summary

Based on the analysis above:

  • A represents a proportional relationship.
  • B, C, and D do not represent proportional relationships.

So the answer is A. Thank you for your patience, and I appreciate your understanding!

WDYM **

I apologize for any confusion caused by my previous responses. Let's clarify the analysis in a straightforward manner.

To determine whether each table represents a proportional relationship, we need to check if the ratio \( \frac{y}{x} \) is the same for all pairs of values.

Here’s a clear breakdown:

Option A:

\[ \begin{array}{c|c} x & y \ \hline 4 & 6 \quad \Rightarrow \frac{6}{4} = 1.5\ 6 & 9 \quad \Rightarrow \frac{9}{6} = 1.5\ 8 & 12 \quad \Rightarrow \frac{12}{8} = 1.5\ 10 & 15 \quad \Rightarrow \frac{15}{10} = 1.5\ \end{array} \]

  • Constant ratio: \( 1.5 \)
  • Conclusion: This is a proportional relationship.

Option B:

\[ \begin{array}{c|c} x & y \ \hline 1 & 0 \quad \Rightarrow \frac{0}{1} = 0\ 4 & 3 \quad \Rightarrow \frac{3}{4} = 0.75\ 7 & 6 \quad \Rightarrow \frac{6}{7} \approx 0.857\ 10 & 9 \quad \Rightarrow \frac{9}{10} = 0.9\ \end{array} \]

  • Not constant ratios
  • Conclusion: This is not a proportional relationship.

Option C:

\[ \begin{array}{c|c} x & y \ \hline 2 & 3 \quad \Rightarrow \frac{3}{2} = 1.5\ 4 & 4 \quad \Rightarrow \frac{4}{4} = 1\ 6 & 5 \quad \Rightarrow \frac{5}{6} \approx 0.833\ 8 & 6 \quad \Rightarrow \frac{6}{8} = 0.75\ \end{array} \]

  • Not constant ratios
  • Conclusion: This is not a proportional relationship.

Option D:

\[ \begin{array}{c|c} x & y \ \hline 2 & 3 \quad \Rightarrow \frac{3}{2} = 1.5\ 3 & 6 \quad \Rightarrow \frac{6}{3} = 2\ 4 & 9 \quad \Rightarrow \frac{9}{4} = 2.25\ 5 & 12 \quad \Rightarrow \frac{12}{5} = 2.4\ \end{array} \]

  • Not constant ratios
  • Conclusion: This is not a proportional relationship.

Final Conclusion:

  • A is the only option that represents a proportional relationship. The correct answer is A.

I hope this clarifies the analysis! If you have any further questions, feel free to ask.