find the graph of this linear function:

\y = -\frac{1}{3}x + 2\

Question

find the graph of this linear function:

\y = -\frac{1}{3}x + 2\

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": true, "concepts_used": [], "new_concepts": [], "current_concepts": [ "Graphing Linear Equations", "Slope-Intercept Form" ] } ## Identify the y-intercept and slope $$ \begin{aligned} &y = mx + b \implies y = -\frac{1}{3}x + 2 \ &\text{y-intercept } (0, b) = (0, 2) \ &\text{slope } m = -\frac{1}{3} \end{aligned} $$ ## Determine key points on the graph $$ \begin{aligned} &\text{For } x = 0: y = 2 \implies (0, 2) \ &\text{For } x = 3: y = -\frac{1}{3}(3) + 2 = 1 \implies (3, 1) \ &\text{For } x = -3: y = -\frac{1}{3}(-3) + 2 = 3 \implies (-3, 3) \end{aligned} $$ ## Match points with the given options $$ \begin{aligned} &\text{First graph points: } (-3, 3), (0, 2), (3, 1) \ &\text{Second graph points: } (-1, 5), (0, 2), (1, -1) \ &\text{Third graph points: } (-3, 4), (0, 2), (3, 0) \end{aligned} $$

(A) The first graph, which passes through $(-3, 3)$, $(0, 2)$, and $(3, 1)$

(B) The second graph, which passes through $(-1, 5)$, $(0, 2)$, and $(1, -1)$

(C) The third graph, which passes through $(-3, 4)$, $(0, 2)$, and $(3, 0)$

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QUESTION IMAGE

Question

Explanation:

Identify the y-intercept and slope

Determine key points on the graph

Match points with the given options

Answer: