Question

ashley started the year with 45 comic books. each month, she adds 5 more comic books to her collection. which table correctly represents y, the number of comic books in her collection, after x months?

Explanation:

<pre_analysis>
{
"quality": "clear",
"question_count": 1,
"skills_matched": [
"step_cot",
"multiple_choice_formatter",
"explain_then_answer",
"quick"
],
"needs_drawing": false,
"concepts_used": [
"Linear Functions",
"Rate of Change",
"y-intercept Interpretation"
],
"new_concepts": [],
"current_concepts": [
"Linear Functions",
"Rate of Change",
"y-intercept Interpretation"
]
}
</pre_analysis>

<reasoning>

Identify the initial value and rate of change

\[

$$\begin{aligned} &\text{Initial value (y-intercept, } b\text{)} = 45\\ &\text{Rate of change (slope, } m\text{)} = 5 \end{aligned}$$

\]

Formulate the linear equation

\[
y = 5x + 45
\]

Evaluate the function for given values of x

\[

$$\begin{aligned} &x = 0 \implies y = 5(0) + 45 = 45\\ &x = 1 \implies y = 5(1) + 45 = 50\\ &x = 2 \implies y = 5(2) + 45 = 55\\ &x = 3 \implies y = 5(3) + 45 = 60 \end{aligned}$$

\]
</reasoning>

<answer>
<mcq-option>(A) Table with \(x = [0, 1, 2, 3]\) and \(y = [5, 50, 95, 140]\)</mcq-option>
<mcq-correct>(B) Table with \(x = [0, 1, 2, 3]\) and \(y = [45, 50, 55, 60]\)</mcq-correct>
<mcq-option>(C) Table with \(x = [0, 5, 10, 15]\) and \(y = [45, 46, 47, 48]\)</mcq-option>
<mcq-option>(D) Table with \(x = [0, 5, 10, 15]\) and \(y = [45, 90, 135, 180]\)</mcq-option>
</answer>

<post_analysis>
{
"subject": "Mathematics",
"question_type": "Multiple Choice",
"knowledge_point": [
"Mathematics",
"Algebra",
"Linear Functions"
]
}
</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": [
"Linear Functions",
"Rate of Change",
"y-intercept Interpretation"
],
"new_concepts": [],
"current_concepts": [
"Linear Functions",
"Rate of Change",
"y-intercept Interpretation"
]
}
</pre_analysis>

<reasoning>

Identify the initial value and rate of change

\[

$$\begin{aligned} &\text{Initial value (y-intercept, } b\text{)} = 45\\ &\text{Rate of change (slope, } m\text{)} = 5 \end{aligned}$$

\]

Formulate the linear equation

\[
y = 5x + 45
\]

Evaluate the function for given values of x

\[

$$\begin{aligned} &x = 0 \implies y = 5(0) + 45 = 45\\ &x = 1 \implies y = 5(1) + 45 = 50\\ &x = 2 \implies y = 5(2) + 45 = 55\\ &x = 3 \implies y = 5(3) + 45 = 60 \end{aligned}$$

\]
</reasoning>

<answer>
<mcq-option>(A) Table with \(x = [0, 1, 2, 3]\) and \(y = [5, 50, 95, 140]\)</mcq-option>
<mcq-correct>(B) Table with \(x = [0, 1, 2, 3]\) and \(y = [45, 50, 55, 60]\)</mcq-correct>
<mcq-option>(C) Table with \(x = [0, 5, 10, 15]\) and \(y = [45, 46, 47, 48]\)</mcq-option>
<mcq-option>(D) Table with \(x = [0, 5, 10, 15]\) and \(y = [45, 90, 135, 180]\)</mcq-option>
</answer>

<post_analysis>
{
"subject": "Mathematics",
"question_type": "Multiple Choice",
"knowledge_point": [
"Mathematics",
"Algebra",
"Linear Functions"
]
}
</post_analysis>