is the function represented by the table linear?

$\begin{array}{|c|c|}\hline x & y \\\hline 10 & -6 \\\hline 11 & 1 \\\hline 12 & 6 \\\hline 13 & 12 \\\hline\end{array}$

yes, because it has a constant rate of change.
yes, because it does not have a constant rate of change.
no, because it has a constant rate of change.
no, because it does not have a constant rate of change.

Question

is the function represented by the table linear?

$\begin{array}{|c|c|}\hline x & y \\\hline 10 & -6 \\\hline 11 & 1 \\\hline 12 & 6 \\\hline 13 & 12 \\\hline\end{array}$

yes, because it has a constant rate of change.
yes, because it does not have a constant rate of change.
no, because it has a constant rate of change.
no, because it does not have a constant rate of change.

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Rate of Change", "Linear Modeling" ], "new_concepts": [], "current_concepts": [ "Linear Functions", "Rate of Change" ] } ## Calculate the rate of change between consecutive points $$ \begin{aligned} &\text{For } (10, -6) \text{ to } (11, 1): \quad \frac{\Delta y}{\Delta x} = \frac{1 - (-6)}{11 - 10} = \frac{7}{1} = 7 \ &\text{For } (11, 1) \text{ to } (12, 6): \quad \frac{\Delta y}{\Delta x} = \frac{6 - 1}{12 - 11} = \frac{5}{1} = 5 \ &\text{For } (12, 6) \text{ to } (13, 12): \quad \frac{\Delta y}{\Delta x} = \frac{12 - 6}{13 - 12} = \frac{6}{1} = 6 \end{aligned} $$ ## Determine if the function is linear $$ \begin{aligned} &7 eq 5 eq 6 \ &\text{The rate of change is not constant.} \ &\text{Therefore, the function is not linear.} \end{aligned} $$

Yes, because it has a constant rate of change.

Yes, because it does not have a constant rate of change.

No, because it has a constant rate of change.

No, because it does not have a constant rate of change.

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

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Question

Explanation:

Calculate the rate of change between consecutive points

Determine if the function is linear

Answer: