the graph represents the number of hours that walter sleeps in terms of the number of days.
which function represents walters situation?
$y = 6x$
$y = 6$
$y = 8$
$y = 8x$

Question

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": [ "Slope of a Line", "Linear Equations" ], "new_concepts": [ "Linear Function Interpretation" ], "current_concepts": [ "Slope of a Line", "Linear Equations", "Linear Function Interpretation" ] } ## Identify key points on the graph Using the *Slope of a Line* knowledge point $$ \begin{aligned} &(x_1, y_1) = (0, 0)\ &(x_2, y_2) = (1, 8)\ &(x_3, y_3) = (2, 16)\ &(x_4, y_4) = (3, 24) \end{aligned} $$ ## Calculate the slope of the line Using the *Slope of a Line* knowledge point $$ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{8 - 0}{1 - 0} = 8 $$ ## Formulate the linear equation Using the *Linear Equations* knowledge point $$ \begin{aligned} &y - y_1 = m(x - x_1)\ &y - 0 = 8(x - 0)\ &y = 8x \end{aligned} $$ ## Verify the function with other points Using the *Linear Equations* knowledge point $$ \begin{aligned} &\text{For } x = 2: \quad y = 8(2) = 16\ &\text{For } x = 3: \quad y = 8(3) = 24 \end{aligned} $$

(A) $y = 6x$

(B) $y = 6$

(C) $y = 8$

(D) $y = 8x$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Linear Function Interpretation" ] }

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QUESTION IMAGE

Question

Explanation:

Identify key points on the graph

Calculate the slope of the line

Formulate the linear equation

Verify the function with other points

Answer: