which graph matches this table?

\begin{tabular}{|c|c|c|c|}
\hline
input (x) & -1 & 0 & 1 \\
\hline
output (y) & 5 & 3 & 1 \\
\hline
\end{tabular}

Question

which graph matches this table?

\begin{tabular}{|c|c|c|c|}
\hline
input (x) & -1 & 0 & 1 \\
\hline
output (y) & 5 & 3 & 1 \\
\hline
\end{tabular}

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": true, "concepts_used": [], "new_concepts": [ "Graphing Linear Equations", "Slope-Intercept Form" ], "current_concepts": [ "Graphing Linear Equations", "Slope-Intercept Form", "Linear Functions" ] } ## Identify points from the table $$ (-1, 5), \quad (0, 3), \quad (1, 1) $$ ## Determine the slope and y-intercept $$ \begin{aligned} m &= \frac{1 - 3}{1 - 0} = -2 \ b &= 3 \end{aligned} $$ ## Match points to the given graphs $$ \begin{aligned} &\text{Graph 1 (left): Passes through } (0, 3) \text{ and } (-1, 1) \implies \text{Incorrect} \ &\text{Graph 2 (middle): Passes through } (-1, 5), (0, 2), (1, -1) \implies \text{Incorrect} \ &\text{Graph 3 (right): Passes through } (-1, 5), (0, 3), (1, 1) \implies \text{Correct} \end{aligned} $$

(A) Left graph: line passing through (-1, 1) and (0, 3)

(B) Middle graph: line passing through (-1, 5) and (0, 2)

(C) Right graph: line passing through (-1, 5), (0, 3), and (1, 1)

{ "elements": [ { "type": "point", "params": [[-1, 5]], "properties": { "name": "(-1, 5)", "size": 4, "color": "#8C55F2", "withLabel": true } }, { "type": "point", "params": [[0, 3]], "properties": { "name": "(0, 3)", "size": 4, "color": "#8C55F2", "withLabel": true } }, { "type": "point", "params": [[1, 1]], "properties": { "name": "(1, 1)", "size": 4, "color": "#8C55F2", "withLabel": true } }, { "type": "functiongraph", "params": [{"js": "-2*x + 3", "latex": "y = -2x + 3"}, -3, 3], "properties": { "strokeColor": "#5583F2", "strokeWidth": 2 } } ] } { "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Graphing Linear Equations" ] }

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Identify points from the table

Determine the slope and y-intercept

Match points to the given graphs

Answer: