which is the graph of the solution set of $5x + 8y 50$?

Question

which is the graph of the solution set of $5x + 8y > 50$?

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": [ "Linear Inequalities", "Boundary Line Intercepts" ], "current_concepts": [ "Linear Inequalities", "Boundary Line Intercepts", "Graphing Inequalities" ] } ## Find the boundary line intercepts $$ \begin{aligned} &5x + 8y = 50\ &\text{For } x = 0: \quad 8y = 50 \implies y = 6.25\ &\text{For } y = 0: \quad 5x = 50 \implies x = 10 \end{aligned} $$ ## Determine the boundary line style $$ \begin{aligned} &5x + 8y > 50 \implies \text{Strict inequality } (>)\ &\text{Boundary line must be dashed} \end{aligned} $$ ## Determine the shaded region $$ \begin{aligned} &\text{Test point } (0,0):\ &5(0) + 8(0) = 0 gtr 50\ &\text{Shade the region not containing } (0,0) \text{ (above/right of the line)} \end{aligned} $$

(A) Dashed line with intercepts at (10, 0) and (0, 6.25), shaded below the line

(B) Dashed line with intercepts at (10, 0) and (0, 6.25), shaded above the line

(C) Solid line with intercepts at (10, 0) and (0, 6.25), shaded above the line

{ "elements": [ { "type": "inequality", "params": [ { "js": "(50 - 5*x)/8", "latex": "5x + 8y > 50" }, [4, 5] ], "properties": { "inverse": true, "strict": true, "strokeColor": "#8C55F2", "strokeWidth": 2, "fillColor": "rgba(140, 85, 242, 0.3)" } }, { "type": "point", "params": [[10, 0]], "properties": { "name": "(10, 0)", "size": 3, "color": "#583C87", "withLabel": true } }, { "type": "point", "params": [[0, 6.25]], "properties": { "name": "(0, 6.25)", "size": 3, "color": "#583C87", "withLabel": true } } ] } { "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Linear Inequalities" ] }

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QUESTION IMAGE

Question

Explanation:

Find the boundary line intercepts

Determine the boundary line style

Determine the shaded region

Answer: