Question

the equation \\(y = 4x\\) represents the relationship between time, \\(x\\), and distance traveled, \\(y\\). which table represents this relationship?

Explanation:

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<reasoning>

Analyze the given relationship

Using the Proportional Relationship Equation knowledge point
\[
y = 4x
\]

Evaluate the first table

Using the Proportional Relationship Equation knowledge point
\[

$$\begin{aligned} &\text{For } x = 0: y = 4(0) = 0 e 4\\ &\text{For } x = 2: y = 4(2) = 8\\ &\text{For } x = 3: y = 4(3) = 12 \end{aligned}$$

\]

Evaluate the second table

Using the Proportional Relationship Equation knowledge point
\[

$$\begin{aligned} &\text{For } x = 1: y = 4(1) = 4\\ &\text{For } x = 2: y = 4(2) = 8\\ &\text{For } x = 3: y = 4(3) = 12 e 16 \end{aligned}$$

\]

Evaluate the third table

Using the Proportional Relationship Equation knowledge point
\[

$$\begin{aligned} &\text{For } x = 1: y = 4(1) = 4\\ &\text{For } x = 4: y = 4(4) = 16 e 8\\ &\text{For } x = 5: y = 4(5) = 20 e 12 \end{aligned}$$

\]

Evaluate the fourth table

Using the Proportional Relationship Equation knowledge point
\[

$$\begin{aligned} &\text{For } x = 2: y = 4(2) = 8\\ &\text{For } x = 4: y = 4(4) = 16\\ &\text{For } x = 8: y = 4(8) = 32 \end{aligned}$$

\]
</reasoning>

<answer>
<mcq-option>(A) Table with rows (0, 4), (2, 8), (3, 12)</mcq-option>
<mcq-option>(B) Table with rows (1, 4), (2, 8), (3, 16)</mcq-option>
<mcq-option>(C) Table with rows (1, 4), (4, 8), (5, 12)</mcq-option>
<mcq-correct>(D) Table with rows (2, 8), (4, 16), (8, 32)</mcq-correct>
</answer>

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"Mathematics",
"Algebra",
"Proportional Relationships"
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</post_analysis>

Answer:

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<reasoning>

Analyze the given relationship

Using the Proportional Relationship Equation knowledge point
\[
y = 4x
\]

Evaluate the first table

Using the Proportional Relationship Equation knowledge point
\[

$$\begin{aligned} &\text{For } x = 0: y = 4(0) = 0 e 4\\ &\text{For } x = 2: y = 4(2) = 8\\ &\text{For } x = 3: y = 4(3) = 12 \end{aligned}$$

\]

Evaluate the second table

Using the Proportional Relationship Equation knowledge point
\[

$$\begin{aligned} &\text{For } x = 1: y = 4(1) = 4\\ &\text{For } x = 2: y = 4(2) = 8\\ &\text{For } x = 3: y = 4(3) = 12 e 16 \end{aligned}$$

\]

Evaluate the third table

Using the Proportional Relationship Equation knowledge point
\[

$$\begin{aligned} &\text{For } x = 1: y = 4(1) = 4\\ &\text{For } x = 4: y = 4(4) = 16 e 8\\ &\text{For } x = 5: y = 4(5) = 20 e 12 \end{aligned}$$

\]

Evaluate the fourth table

Using the Proportional Relationship Equation knowledge point
\[

$$\begin{aligned} &\text{For } x = 2: y = 4(2) = 8\\ &\text{For } x = 4: y = 4(4) = 16\\ &\text{For } x = 8: y = 4(8) = 32 \end{aligned}$$

\]
</reasoning>

<answer>
<mcq-option>(A) Table with rows (0, 4), (2, 8), (3, 12)</mcq-option>
<mcq-option>(B) Table with rows (1, 4), (2, 8), (3, 16)</mcq-option>
<mcq-option>(C) Table with rows (1, 4), (4, 8), (5, 12)</mcq-option>
<mcq-correct>(D) Table with rows (2, 8), (4, 16), (8, 32)</mcq-correct>
</answer>

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