Question

which equation represents a proportional relationship that has a constant of proportionality equal to 0.7?

\\(\frac{y}{x} = \frac{7}{10}\\)

\\(\frac{y}{x} = \frac{1}{7}\\)

\\(xy = \frac{7}{10}\\)

\\(xy = \frac{1}{7}\\)

Explanation:

<pre_analysis>
{
"quality": "clear",
"question_count": 1,
"skills_matched": [
"step_cot",
"multiple_choice_formatter",
"explain_then_answer",
"tutor",
"mastery_adaptive_brevity"
],
"needs_drawing": false,
"concepts_used": [
"Constant of Proportionality",
"Proportional Relationship Equation"
],
"new_concepts": [],
"current_concepts": [
"Constant of Proportionality",
"Proportional Relationship Equation"
]
}
</pre_analysis>

<reasoning>

Define proportional relationships

Using the Constant of Proportionality and Proportional Relationship Equation knowledge points
\[

$$\begin{aligned} &\frac{y}{x} = k \quad \text{or} \quad y = kx\\ &k = 0.7 \end{aligned}$$

\]

Convert decimal to fraction

Using the Constant of Proportionality knowledge point
\[
0.7 = \frac{7}{10}
\]

Substitute constant into equation

Using the Proportional Relationship Equation knowledge point
\[
\frac{y}{x} = \frac{7}{10}
\]
</reasoning>

<answer>
<mcq-correct>(A) \(\frac{y}{x} = \frac{7}{10}\)</mcq-correct>
<mcq-option>(B) \(\frac{y}{x} = \frac{1}{7}\)</mcq-option>
<mcq-option>(C) \(xy = \frac{7}{10}\)</mcq-option>
<mcq-option>(D) \(xy = \frac{1}{7}\)</mcq-option>
</answer>

<post_analysis>
{
"subject": "Mathematics",
"question_type": "Multiple Choice",
"knowledge_point": [
"Mathematics",
"Algebra",
"Proportional Relationship Equation"
]
}
</post_analysis>

Answer:

<pre_analysis>
{
"quality": "clear",
"question_count": 1,
"skills_matched": [
"step_cot",
"multiple_choice_formatter",
"explain_then_answer",
"tutor",
"mastery_adaptive_brevity"
],
"needs_drawing": false,
"concepts_used": [
"Constant of Proportionality",
"Proportional Relationship Equation"
],
"new_concepts": [],
"current_concepts": [
"Constant of Proportionality",
"Proportional Relationship Equation"
]
}
</pre_analysis>

<reasoning>

Define proportional relationships

Using the Constant of Proportionality and Proportional Relationship Equation knowledge points
\[

$$\begin{aligned} &\frac{y}{x} = k \quad \text{or} \quad y = kx\\ &k = 0.7 \end{aligned}$$

\]

Convert decimal to fraction

Using the Constant of Proportionality knowledge point
\[
0.7 = \frac{7}{10}
\]

Substitute constant into equation

Using the Proportional Relationship Equation knowledge point
\[
\frac{y}{x} = \frac{7}{10}
\]
</reasoning>

<answer>
<mcq-correct>(A) \(\frac{y}{x} = \frac{7}{10}\)</mcq-correct>
<mcq-option>(B) \(\frac{y}{x} = \frac{1}{7}\)</mcq-option>
<mcq-option>(C) \(xy = \frac{7}{10}\)</mcq-option>
<mcq-option>(D) \(xy = \frac{1}{7}\)</mcq-option>
</answer>

<post_analysis>
{
"subject": "Mathematics",
"question_type": "Multiple Choice",
"knowledge_point": [
"Mathematics",
"Algebra",
"Proportional Relationship Equation"
]
}
</post_analysis>