Question

harrys soccer team plays 2 nonconference games for every 3 games that they play against conference opponents. if \\(y\\) represents the number of nonconference games and \\(x\\) represents the number of conference games, which equation best models this proportional relationship?

\\(y = \frac{2}{3}x\\)

\\(y = \frac{3}{2}x\\)

\\(y = 2x\\)

\\(y = 6x\\)

Explanation:

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<reasoning>

Identify the variables and given ratio

Using the Constant of Proportionality knowledge point
\[

$$\begin{aligned} &y = \text{number of nonconference games}\\ &x = \text{number of conference games}\\ &\text{Ratio of } y \text{ to } x = \frac{2}{3} \end{aligned}$$

\]

Determine the constant of proportionality

Using the Constant of Proportionality knowledge point
\[

$$\begin{aligned} &k = \frac{y}{x} = \frac{2}{3} \end{aligned}$$

\]

Write the proportional relationship equation

Using the Proportional Relationship Equation knowledge point
\[

$$\begin{aligned} &y = kx\\ &y = \frac{2}{3}x \end{aligned}$$

\]
</reasoning>

<answer>
<mcq-correct>(A) \(y = \frac{2}{3}x\)</mcq-correct>
<mcq-option>(B) \(y = \frac{3}{2}x\)</mcq-option>
<mcq-option>(C) \(y = 2x\)</mcq-option>
<mcq-option>(D) \(y = 6x\)</mcq-option>
</answer>

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"Mathematics",
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]
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Answer:

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<reasoning>

Identify the variables and given ratio

Using the Constant of Proportionality knowledge point
\[

$$\begin{aligned} &y = \text{number of nonconference games}\\ &x = \text{number of conference games}\\ &\text{Ratio of } y \text{ to } x = \frac{2}{3} \end{aligned}$$

\]

Determine the constant of proportionality

Using the Constant of Proportionality knowledge point
\[

$$\begin{aligned} &k = \frac{y}{x} = \frac{2}{3} \end{aligned}$$

\]

Write the proportional relationship equation

Using the Proportional Relationship Equation knowledge point
\[

$$\begin{aligned} &y = kx\\ &y = \frac{2}{3}x \end{aligned}$$

\]
</reasoning>

<answer>
<mcq-correct>(A) \(y = \frac{2}{3}x\)</mcq-correct>
<mcq-option>(B) \(y = \frac{3}{2}x\)</mcq-option>
<mcq-option>(C) \(y = 2x\)</mcq-option>
<mcq-option>(D) \(y = 6x\)</mcq-option>
</answer>

<post_analysis>
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"question_type": "Multiple Choice",
"knowledge_point": [
"Mathematics",
"Algebra",
"Proportional Relationships"
]
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