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{ "quality": "blurry", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Linear Modeling", "Average Rate of Change" ], "new_concepts": [ "Linear Function Identification" ], "current_concepts": [ "Linear Modeling", "Average Rate of Change", "Linear Function Identification" ] } ## Check rate of change for first table Using the *Average Rate of Change* knowledge point $$ \begin{aligned} &\text{Points: } (-3, 0), (-1, 2), (1, 2), (2, 4), (3, 6)\ &m_1 = \frac{2 - 0}{-1 - (-3)} = \frac{2}{2} = 1\ &m_2 = \frac{2 - 2}{1 - (-1)} = \frac{0}{2} = 0 \quad (\text{Not constant}) \end{aligned} $$ ## Check rate of change for second table Using the *Average Rate of Change* and *Linear Modeling* knowledge points $$ \begin{aligned} &\text{Points: } (-6, -10), (-2, -4), (0, -1), (2, 2), (3, 3.5)\ &m_1 = \frac{-4 - (-10)}{-2 - (-6)} = \frac{6}{4} = 1.5\ &m_2 = \frac{-1 - (-4)}{0 - (-2)} = \frac{3}{2} = 1.5\ &m_3 = \frac{2 - (-1)}{2 - 0} = \frac{3}{2} = 1.5\ &m_4 = \frac{3.5 - 2}{3 - 2} = \frac{1.5}{1} = 1.5 \quad (\text{Constant rate of change}) \end{aligned} $$ ## Check rate of change for third table Using the *Average Rate of Change* knowledge point $$ \begin{aligned} &\text{Points: } (0, -2), (1, 0), (2, 2), (3, 7), (4, 14)\ &m_1 = \frac{0 - (-2)}{1 - 0} = 2\ &m_2 = \frac{2 - 0}{2 - 1} = 2\ &m_3 = \frac{7 - 2}{3 - 2} = 5 \quad (\text{Not constant}) \end{aligned} $$

(A) Table 1: $(-3, 0), (-1, 2), (1, 2), (2, 4), (3, 6)$

(B) Table 2: $(-6, -10), (-2, -4), (0, -1), (2, 2), (3, 3.5)$

(C) Table 3: $(0, -2), (1, 0), (2, 2), (3, 7), (4, 14)$

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

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Explanation:

Check rate of change for first table

Check rate of change for second table

Check rate of change for third table

Answer: