graph the line.

\-2x + y = -8\

Question

graph the line.

\-2x + y = -8\

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "explain_then_answer", "quick" ], "needs_drawing": true, "concepts_used": [ "Graphing Linear Equations" ], "new_concepts": [], "current_concepts": [ "Graphing Linear Equations" ] } ## Find the intercepts of the line $$ \begin{aligned} &\text{Let } x = 0:\ &-2(0) + y = -8 \implies y = -8 \quad \implies (0, -8)\ &\text{Let } y = 0:\ &-2x + 0 = -8 \implies x = 4 \quad \implies (4, 0) \end{aligned} $$ ## Rewrite in slope-intercept form $$ \begin{aligned} &-2x + y = -8\ &y = 2x - 8 \end{aligned} $$ ## Identify key graphing points $$ \begin{aligned} &\text{Point 1: } (4, 0)\ &\text{Point 2: } (0, -8)\ &\text{Point 3: } (5, 2) \end{aligned} $$ To graph the line $-2x + y = -8$, plot the $x$-intercept at $(4, 0)$ and the $y$-intercept at $(0, -8)$, then draw a straight line passing through these points. { "elements": [ { "type": "point", "params": [[4, 0]], "properties": { "name": "(4, 0)", "size": 4, "color": "#8C55F2", "withLabel": true } }, { "type": "point", "params": [[0, -8]], "properties": { "name": "(0, -8)", "size": 4, "color": "#8C55F2", "withLabel": true } }, { "type": "line", "params": [[4, 0], [0, -8]], "properties": { "strokeColor": "#5583F2", "strokeWidth": 3 } } ] } { "subject": "Mathematics", "question_type": "Free Response", "knowledge_point": [ "Mathematics", "Geometry", "Graphing Linear Equations" ] }

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Question

Explanation:

Find the intercepts of the line

Rewrite in slope-intercept form

Identify key graphing points

Answer: