\
\begin{aligned}
&f(8) = -5 \\
&f(16) = -11
\end{aligned}
\
if it follow a linear function, what the slope $\frac{\text{change in } y}{\text{change in } x} = \frac{y_2 - y_1}{x_2 - x_1}$

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Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Linear Function", "Slope Formula", "Function Notation" ], "new_concepts": [], "current_concepts": [ "Linear Function", "Slope Formula", "Function Notation" ] } ## Interpret the given function notation Using the *Function Notation* knowledge point $$ \begin{aligned} &f(8) = -5 \implies (x_1, y_1) = (8, -5)\ &f(10) = -11 \implies (x_2, y_2) = (10, -11) \end{aligned} $$ ## Apply the slope formula Using the *Slope Formula* and *Linear Function* knowledge points $$ \begin{aligned} m &= \frac{y_2 - y_1}{x_2 - x_1}\ m &= \frac{-11 - (-5)}{10 - 8}\ m &= \frac{-11 + 5}{2}\ m &= \frac{-6}{2}\ m &= -3 \end{aligned} $$ The slope of the linear function is $-3$. { "subject": "Mathematics", "question_type": "Free Response", "knowledge_point": [ "Mathematics", "Algebra", "Linear Function" ] }

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Explanation:

Interpret the given function notation

Apply the slope formula

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