which table shows a linear function?

Question

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" ], "new_concepts": [], "current_concepts": [ "Linear Functions", "Tabular Representations", "Average Rate of Change" ] } ## Calculate rates of change for the first table $$ \begin{aligned} &\text{Points: } (-5, -4), (-3, -3), (-1, -2), (1, 2), (2, 5)\ &m_1 = \frac{-3 - (-4)}{-3 - (-5)} = \frac{1}{2}\ &m_2 = \frac{-2 - (-3)}{-1 - (-3)} = \frac{1}{2}\ &m_3 = \frac{2 - (-2)}{1 - (-1)} = \frac{4}{2} = 2 \quad (\text{Not constant}) \end{aligned} $$ ## Calculate rates of change for the second table $$ \begin{aligned} &\text{Points: } (-4, 3), (-3, 0), (-2, -1), (1, -3), (2, -5)\ &m_1 = \frac{0 - 3}{-3 - (-4)} = -3\ &m_2 = \frac{-1 - 0}{-2 - (-3)} = -1 \quad (\text{Not constant}) \end{aligned} $$ ## Calculate rates of change for the third table $$ \begin{aligned} &\text{Points: } (-5, -2), (-3, 0), (-1, 2), (0, 3), (2, 5)\ &m_1 = \frac{0 - (-2)}{-3 - (-5)} = \frac{2}{2} = 1\ &m_2 = \frac{2 - 0}{-1 - (-3)} = \frac{2}{2} = 1\ &m_3 = \frac{3 - 2}{0 - (-1)} = \frac{1}{1} = 1\ &m_4 = \frac{5 - 3}{2 - 0} = \frac{2}{2} = 1 \quad (\text{Constant rate of change } m = 1) \end{aligned} $$

(A) Table 1: | x | y | |---|---| | -5 | -4 | | -3 | -3 | | -1 | -2 | | 1 | 2 | | 2 | 5 |

(B) Table 2: | x | y | |---|---| | -4 | 3 | | -3 | 0 | | -2 | -1 | | 1 | -3 | | 2 | -5 |

(C) Table 3: | x | y | |---|---| | -5 | -2 | | -3 | 0 | | -1 | 2 | | 0 | 3 | | 2 | 5 |

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

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QUESTION IMAGE

Question

Explanation:

Calculate rates of change for the first table

Calculate rates of change for the second table

Calculate rates of change for the third table

Answer:

x	y
-3	0
-1	2
0	3
2	5	(Correct answer)**