tickets for the school play sell for $4 each. which graph shows the relationship between the number of tickets sold (x) and the total income from the tickets (y)?

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Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": true, "concepts_used": [ "Direct Variation Graphs", "Linear Modeling" ], "new_concepts": [], "current_concepts": [ "Direct Variation Graphs", "Linear Modeling" ] } ## Formulate the linear relationship $$ y = 4x $$ ## Determine key points on the graph $$ \begin{aligned} x = 0 &\implies y = 0 \ x = 1 &\implies y = 4 \ x = 2 &\implies y = 8 \ x = 3 &\implies y = 12 \end{aligned} $$ ## Identify the correct graph matching the points $$ \text{The correct graph must pass through } (0,0), (1,4), (2,8), \text{ and } (3,12). $$

(A) A graph passing through the origin $(0,0)$ with a steep slope passing through $(1,4)$, $(2,8)$, and $(3,12)$

(B) A graph passing through the origin $(0,0)$ with a shallow slope passing through $(4,1)$ and $(8,2)$

{ "elements": [ { "type": "functiongraph", "params": [ { "js": "4*x", "latex": "y = 4x" }, 0, 4 ], "properties": { "strokeColor": "#8C55F2", "strokeWidth": 3, "name": "y = 4x", "withLabel": true } }, { "type": "point", "params": [[0, 0]], "properties": { "name": "(0,0)", "size": 4, "color": "#583C87", "withLabel": true } }, { "type": "point", "params": [[1, 4]], "properties": { "name": "(1,4)", "size": 4, "color": "#583C87", "withLabel": true } }, { "type": "point", "params": [[2, 8]], "properties": { "name": "(2,8)", "size": 4, "color": "#583C87", "withLabel": true } }, { "type": "point", "params": [[3, 12]], "properties": { "name": "(3,12)", "size": 4, "color": "#583C87", "withLabel": true } } ], "timestamps": [0.5, 1.0, 1.5] } { "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Direct Variation Graphs" ] }

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Question

Explanation:

Formulate the linear relationship

Determine key points on the graph

Identify the correct graph matching the points

Answer: