distance (in miles)
time (in hours)
$f(x)$
$(0, 0)$
$(5, 1)$
$(9, 6)$
$(11, 11)$

$\frac{2}{5}$
1
2
$\frac{5}{2}$

Question

distance (in miles)
time (in hours)
$f(x)$
$(0, 0)$
$(5, 1)$
$(9, 6)$
$(11, 11)$

$\frac{2}{5}$
1
2
$\frac{5}{2}$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Average Rate of Change", "Average Rate of Change on Interval" ], "new_concepts": [], "current_concepts": [ "Average Rate of Change", "Average Rate of Change on Interval", "Graphical Analysis" ] } ## Identify the interval and coordinates from the graph $$ \begin{aligned} &\text{Interval: } [9, 11]\ &\text{Point at } x = 9: (9, 6)\ &\text{Point at } x = 11: (11, 11) \end{aligned} $$ ## Calculate the average rate of change $$ \begin{aligned} \text{Average Rate of Change} &= \frac{f(11) - f(9)}{11 - 9} \ &= \frac{11 - 6}{11 - 9} \ &= \frac{5}{2} \end{aligned} $$

(A) $\frac{2}{5}$

(B) $1$

(C) $2$

(D) $\frac{5}{2}$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Average Rate of Change on Interval" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the interval and coordinates from the graph

Calculate the average rate of change

Answer: