Question

question 19 points 2

find the function which has greater rate of change.

\\(y = 5x + 2\\)

\\(y = 3x - 5\\)

Explanation:

<pre_analysis>
{
"quality": "clear",
"question_count": 1,
"skills_matched": [
"step_cot",
"multiple_choice_formatter",
"explain_then_answer",
"quick"
],
"needs_drawing": false,
"concepts_used": [
"Slope-Intercept Form",
"Slope of a Linear Function",
"Rate of Change Comparison"
],
"new_concepts": [],
"current_concepts": [
"Slope-Intercept Form",
"Slope of a Linear Function",
"Rate of Change Comparison"
]
}
</pre_analysis>

<reasoning>

Identify the rate of change for each linear function

\[

$$\begin{aligned} &\text{For } y = 5x + 2: \quad m_1 = 5 \\ &\text{For } y = 3x - 5: \quad m_2 = 3 \end{aligned}$$

\]

Compare the rates of change

\[
5 > 3 \implies m_1 > m_2
\]
</reasoning>

<answer>
<mcq-correct>(A) \(y = 5x + 2\)</mcq-correct>
<mcq-option>(B) \(y = 3x - 5\)</mcq-option>
</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",
"quick"
],
"needs_drawing": false,
"concepts_used": [
"Slope-Intercept Form",
"Slope of a Linear Function",
"Rate of Change Comparison"
],
"new_concepts": [],
"current_concepts": [
"Slope-Intercept Form",
"Slope of a Linear Function",
"Rate of Change Comparison"
]
}
</pre_analysis>

<reasoning>

Identify the rate of change for each linear function

\[

$$\begin{aligned} &\text{For } y = 5x + 2: \quad m_1 = 5 \\ &\text{For } y = 3x - 5: \quad m_2 = 3 \end{aligned}$$

\]

Compare the rates of change

\[
5 > 3 \implies m_1 > m_2
\]
</reasoning>

<answer>
<mcq-correct>(A) \(y = 5x + 2\)</mcq-correct>
<mcq-option>(B) \(y = 3x - 5\)</mcq-option>
</answer>

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