Question

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

Answer 1

wtf is **

the answers are A B C or D

Answer 2

WDYM **

Answer 3

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.

Answer 4

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!

Answer 5

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.