house sales
number of houses sold
$f(x)$
$(2, 8)$
$(6, 6)$
$(12, 4)$
$(0, 0)$
$(10, 2)$
number of days

$-\frac{4}{3}$
$-\frac{3}{4}$
6
8

Question

house sales
number of houses sold
$f(x)$
$(2, 8)$
$(6, 6)$
$(12, 4)$
$(0, 0)$
$(10, 2)$
number of days

$-\frac{4}{3}$
$-\frac{3}{4}$
6
8

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Graph Interpretation", "Function Behavior" ], "new_concepts": [ "Average Rate of Change", "Secant Line Slope" ], "current_concepts": [ "Graph Interpretation", "Function Behavior", "Average Rate of Change" ] } ## Identify the interval and coordinates Using the **Graph Interpretation** and **Function Behavior** knowledge points $$ \begin{aligned} &\text{Interval: } [2, 10]\ &x_1 = 2 \implies f(2) = 8\ &x_2 = 10 \implies f(10) = 2 \end{aligned} $$ ## Calculate the average rate of change Using the **Function Behavior** knowledge point $$ \begin{aligned} \text{Average Rate of Change} &= \frac{f(10) - f(2)}{10 - 2} \ &= \frac{2 - 8}{10 - 2} \ &= \frac{-6}{8} \ &= -\frac{3}{4} \end{aligned} $$

(A) $-\frac{4}{3}$

(B) $-\frac{3}{4}$

(C) $6$

(D) $8$

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

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QUESTION IMAGE

Question

Explanation:

Identify the interval and coordinates

Calculate the average rate of change

Answer: