8. step 2: complete the table for $y

Question

8. step 2: complete the table for $y < -x + 4$.

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [], "new_concepts": [ "Linear Equation Tables", "Graphing Linear Inequalities" ], "current_concepts": [ "Linear Equation Tables", "Graphing Linear Inequalities" ] } ## Identify the boundary equation and standard input values $$ \begin{aligned} &y = -x + 4\ &x \in \{1, 2, 3\} \end{aligned} $$ ## Calculate corresponding y-values $$ \begin{aligned} &x = 1 \implies y = -(1) + 4 = 3\ &x = 2 \implies y = -(2) + 4 = 2\ &x = 3 \implies y = -(3) + 4 = 1 \end{aligned} $$ ## Match with the given options $$ \begin{aligned} &\text{Option 1 (top): } y \in \{5, 3, 1\} \implies \text{Incorrect}\ &\text{Option 2 (middle-top): } y \in \{3, 7, 11\} \implies \text{Incorrect}\ &\text{Option 3 (middle-bottom): } y \in \{3, 4, 5\} \implies \text{Incorrect}\ &\text{Option 4 (bottom, partially visible): } y \in \{3, 2, 1\} \implies \text{Correct} \end{aligned} $$

(A) Table with y-values: 5, 3, 1

(B) Table with y-values: 3, 7, 11

(C) Table with y-values: 3, 4, 5

(D) Table with y-values: 3, 2, 1

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

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QUESTION IMAGE

Question

Explanation:

Identify the boundary equation and standard input values

Calculate corresponding y-values

Match with the given options

Answer: