the graph shows the distance in miles of a runner over $x$ hours. what is the average rate of speed over the interval $9, 11$?

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{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Average Rate of Change" ], "new_concepts": [], "current_concepts": [ "Average Rate of Change", "Rate of Change Interpretation" ] } ## Identify the coordinates from the graph Using the *Average Rate of Change* knowledge point $$ \begin{aligned} &(x_1, y_1) = (9, 6)\ &(x_2, y_2) = (11, 11) \end{aligned} $$ ## Calculate the average rate of change Using the *Average Rate of Change* knowledge point $$ \begin{aligned} \text{Average Rate of Speed} &= \frac{y_2 - y_1}{x_2 - x_1} \ &= \frac{11 - 6}{11 - 9} \ &= \frac{5}{2} \ &= 2.5\text{ miles per hour} \end{aligned} $$ $2.5$ miles per hour { "subject": "Mathematics", "question_type": "Free Response", "knowledge_point": [ "Mathematics", "Algebra", "Average Rate of Change" ] }

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Identify the coordinates from the graph

Calculate the average rate of change

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