Question

question 30 points 3

choose the table of values which has greater rate of change.

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": [
"Rate of Change Comparison"
],
"new_concepts": [],
"current_concepts": [
"Rate of Change Comparison"
]
}
</pre_analysis>

<reasoning>

Calculate rate of change for the first table

Using the Rate of Change Comparison knowledge point
\[
m_1 = \frac{6 - 3}{2 - 1} = 3
\]

Calculate rate of change for the second table

Using the Rate of Change Comparison knowledge point
\[
m_2 = \frac{10 - 5}{2 - 1} = 5
\]

Compare the rates of change

Using the Rate of Change Comparison knowledge point
\[
5 > 3 \implies m_2 > m_1
\]
</reasoning>

<answer>
<mcq-option>(A) Table 1: x = [1, 2, 3], y = [3, 6, 9]</mcq-option>
<mcq-correct>(B) Table 2: x = [1, 2, 3], y = [5, 10, 15]</mcq-correct>
</answer>

<post_analysis>
{
"subject": "Mathematics",
"question_type": "Multiple Choice",
"knowledge_point": [
"Mathematics",
"Algebra",
"Rate of Change Comparison"
]
}
</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": [
"Rate of Change Comparison"
],
"new_concepts": [],
"current_concepts": [
"Rate of Change Comparison"
]
}
</pre_analysis>

<reasoning>

Calculate rate of change for the first table

Using the Rate of Change Comparison knowledge point
\[
m_1 = \frac{6 - 3}{2 - 1} = 3
\]

Calculate rate of change for the second table

Using the Rate of Change Comparison knowledge point
\[
m_2 = \frac{10 - 5}{2 - 1} = 5
\]

Compare the rates of change

Using the Rate of Change Comparison knowledge point
\[
5 > 3 \implies m_2 > m_1
\]
</reasoning>

<answer>
<mcq-option>(A) Table 1: x = [1, 2, 3], y = [3, 6, 9]</mcq-option>
<mcq-correct>(B) Table 2: x = [1, 2, 3], y = [5, 10, 15]</mcq-correct>
</answer>

<post_analysis>
{
"subject": "Mathematics",
"question_type": "Multiple Choice",
"knowledge_point": [
"Mathematics",
"Algebra",
"Rate of Change Comparison"
]
}
</post_analysis>