13. the graph of $y = -\frac{1}{4}x + 4$ is shown on the grid.

choose the ordered pairs that are in the solution set of $y -\frac{1}{4}x + 4$.

$(0, 0)$ $(-7, 9)$ $(0, 8)$ $(4, 3)$ $(9, 1)$ $(5, 5)$

Question

13. the graph of $y = -\frac{1}{4}x + 4$ is shown on the grid.

choose the ordered pairs that are in the solution set of $y > -\frac{1}{4}x + 4$.

$(0, 0)$ $(-7, 9)$ $(0, 8)$ $(4, 3)$ $(9, 1)$ $(5, 5)$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "explain_then_answer", "quick" ], "needs_drawing": true, "concepts_used": [ "Linear Inequalities", "Ordered Pairs" ], "new_concepts": [], "current_concepts": [ "Linear Inequalities", "Ordered Pairs" ] } ## Define the inequality and candidate points $$ y > -\frac{1}{4}x + 4 $$ Candidate points: $(0,0)$, $(-7,9)$, $(0,8)$, $(4,3)$, $(9,1)$, $(5,5)$ ## Evaluate each ordered pair $$ \begin{aligned} (0,0): \quad & 0 > -\frac{1}{4}(0) + 4 \implies 0 > 4 \quad (\text{False}) \ (-7,9): \quad & 9 > -\frac{1}{4}(-7) + 4 \implies 9 > 1.75 + 4 \implies 9 > 5.75 \quad (\text{True}) \ (0,8): \quad & 8 > -\frac{1}{4}(0) + 4 \implies 8 > 4 \quad (\text{True}) \ (4,3): \quad & 3 > -\frac{1}{4}(4) + 4 \implies 3 > -1 + 4 \implies 3 > 3 \quad (\text{False}) \ (9,1): \quad & 1 > -\frac{1}{4}(9) + 4 \implies 1 > -2.25 + 4 \implies 1 > 1.75 \quad (\text{False}) \ (5,5): \quad & 5 > -\frac{1}{4}(5) + 4 \implies 5 > -1.25 + 4 \implies 5 > 2.75 \quad (\text{True}) \end{aligned} $$ ## Identify the valid solution set The ordered pairs that satisfy the inequality are: $$ (-7,9), \quad (0,8), \quad (5,5) $$ $(-7,9)$, $(0,8)$, and $(5,5)$ { "elements": [ { "type": "inequality", "params": [ { "js": "-0.25*x + 4", "latex": "y > -\frac{1}{4}x + 4" }, [0, 6] ], "properties": { "inverse": true, "strict": true, "fillColor": "rgba(140, 85, 242, 0.3)", "strokeColor": "#8C55F2", "strokeWidth": 2, "dash": 2 } }, { "type": "point", "params": [[0, 0]], "properties": { "name": "(0,0)", "color": "#F2557F", "size": 3, "withLabel": true } }, { "type": "point", "params": [[-7, 9]], "properties": { "name": "(-7,9)", "color": "#5583F2", "size": 3, "withLabel": true } }, { "type": "point", "params": [[0, 8]], "properties": { "name": "(0,8)", "color": "#5583F2", "size": 3, "withLabel": true } }, { "type": "point", "params": [[4, 3]], "properties": { "name": "(4,3)", "color": "#F2557F", "size": 3, "withLabel": true } }, { "type": "point", "params": [[9, 1]], "properties": { "name": "(9,1)", "color": "#F2557F", "size": 3, "withLabel": true } }, { "type": "point", "params": [[5, 5]], "properties": { "name": "(5,5)", "color": "#5583F2", "size": 3, "withLabel": true } } ] } { "subject": "Mathematics", "question_type": "Free Response", "knowledge_point": [ "Mathematics", "Algebra", "Linear Inequalities" ] }

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Question

Explanation:

Define the inequality and candidate points

Evaluate each ordered pair

Identify the valid solution set

Answer: