the table represents the cost of flowers at the tigerlily flower shop.

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{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": true, "concepts_used": [ "Linear Equation from Table", "Discrete Graph" ], "new_concepts": [ "Non-linear Data Analysis" ], "current_concepts": [ "Linear Equation from Table", "Discrete Graph", "Non-linear Data Analysis" ] } ## Analyze the rate of change Using the *Linear Equation from Table* knowledge point $$ \begin{aligned} &\text{Let } q \text{ be the quantity and } P \text{ be the price.}\ &\text{For } q = 1 \text{ to } 2: \Delta P = 3.50 - 2.00 = 1.50\ &\text{For } q = 2 \text{ to } 3: \Delta P = 5.00 - 3.50 = 1.50\ &\text{For } q = 3 \text{ to } 4: \Delta P = 6.50 - 5.00 = 1.50\ &\text{For } q = 4 \text{ to } 5: \Delta P = 8.00 - 6.50 = 1.50\ &\text{For } q = 5 \text{ to } 6: \Delta P = 9.00 - 8.00 = 1.00 \end{aligned} $$ ## Determine the relationship type Using the *Discrete Graph* knowledge point $$ \begin{aligned} &\text{The rate of change is constant at } \$1.50 \text{ per flower for } q \in [1, 5].\ &\text{At } q = 6\text{, the rate of change decreases to } \$1.00.\ &\text{Because the rate of change is not constant throughout, the relationship is non-linear.}\ &\text{Since quantity represents individual flowers, the data is discrete.} \end{aligned} $$ The table represents a discrete, non-linear relationship. The price increases by a constant rate of \$1.50 per flower for quantities 1 through 5, but the rate of change decreases to \$1.00 when purchasing the 6th flower. { "elements": [ { "type": "point", "params": [[1, 2.00]], "properties": { "name": "(1, 2.00)", "size": 4, "color": "#8C55F2", "withLabel": true } }, { "type": "point", "params": [[2, 3.50]], "properties": { "name": "(2, 3.50)", "size": 4, "color": "#8C55F2", "withLabel": true } }, { "type": "point", "params": [[3, 5.00]], "properties": { "name": "(3, 5.00)", "size": 4, "color": "#8C55F2", "withLabel": true } }, { "type": "point", "params": [[4, 6.50]], "properties": { "name": "(4, 6.50)", "size": 4, "color": "#8C55F2", "withLabel": true } }, { "type": "point", "params": [[5, 8.00]], "properties": { "name": "(5, 8.00)", "size": 4, "color": "#8C55F2", "withLabel": true } }, { "type": "point", "params": [[6, 9.00]], "properties": { "name": "(6, 9.00)", "size": 4, "color": "#F2557F", "withLabel": true } } ], "timestamps": [0.2, 0.4, 0.6, 0.8, 1.0, 1.2] } { "subject": "Mathematics", "question_type": "Free Response", "knowledge_point": [ "Mathematics", "Algebra", "Linear Equation from Table" ] }

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Analyze the rate of change

Determine the relationship type

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