5 which graph represents $y - 3 = -x$?

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Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": true, "concepts_used": [ "Linear Graphing" ], "new_concepts": [ "Slope-Intercept Form" ], "current_concepts": [ "Linear Graphing", "Slope-Intercept Form" ] } ## Rewrite the equation in slope-intercept form $$ \begin{aligned} y - 3 &= -x \ y &= -x + 3 \end{aligned} $$ ## Identify key features of the linear equation $$ \begin{aligned} \text{Slope } (m) &= -1 \ y\text{-intercept } (b) &= 3 \implies (0, 3) \ x\text{-intercept } (y=0) &\implies 0 = -x + 3 \implies x = 3 \implies (3, 0) \end{aligned} $$ ## Match features with the given graphs $$ \begin{aligned} \text{Graph A: } & y\text{-intercept is } (0, -3) \ \text{Graph B: } & \text{Horizontal line } y = -3 \ \text{Graph C: } & y\text{-intercept is } (0, 3), \text{ passes through } (3, 0) \ \text{Graph D: } & \text{Horizontal line } y = 3 \end{aligned} $$

(A) Line with y-intercept at (0, -3)

(B) Horizontal line at y = -3

(C) Line with y-intercept at (0, 3) and x-intercept at (3, 0)

(D) Horizontal line at y = 3

{ "elements": [ { "type": "functiongraph", "params": [ { "js": "-x + 3", "latex": "y = -x + 3" }, -10, 10 ], "properties": { "strokeColor": "#8C55F2", "strokeWidth": 3, "name": "y - 3 = -x", "withLabel": true } }, { "type": "point", "params": [ [0, 3] ], "properties": { "name": "(0, 3)", "size": 4, "color": "#F2557F", "withLabel": true } }, { "type": "point", "params": [ [3, 0] ], "properties": { "name": "(3, 0)", "size": 4, "color": "#F2557F", "withLabel": true } } ], "timestamps": [0.5, 1.0] } { "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Geometry", "Linear Graphing" ] }

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Question

Explanation:

Rewrite the equation in slope-intercept form

Identify key features of the linear equation

Match features with the given graphs

Answer: