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?

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Accepted Answer

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

(A) Table with $x = [0, 1, 2, 3]$ and $y = [5, 50, 95, 140]$

(B) Table with $x = [0, 1, 2, 3]$ and $y = [45, 50, 55, 60]$

(C) Table with $x = [0, 5, 10, 15]$ and $y = [45, 46, 47, 48]$

(D) Table with $x = [0, 5, 10, 15]$ and $y = [45, 90, 135, 180]$

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

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Explanation:

Identify the initial value and rate of change

Formulate the linear equation

Evaluate the function for given values of x

Answer: