eula needs to buy binders that cost \$4 each and notebooks that cost \$2 each. she has \$20. the inequality $4x + 2y \le 20$ represents the situation, where $x$ represents the number of binders and $y$ represents the number of notebooks.

step 1: identify the $x$- and $y$-intercepts of the boundary line.
when $x = 0$, $y = $
when $y = 0$, $x = $

Question

eula needs to buy binders that cost \$4 each and notebooks that cost \$2 each. she has \$20. the inequality $4x + 2y \le 20$ represents the situation, where $x$ represents the number of binders and $y$ represents the number of notebooks.

step 1: identify the $x$- and $y$-intercepts of the boundary line.
when $x = 0$, $y = $
when $y = 0$, $x = $

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": true, "concepts_used": [ "Linear Inequalities", "Boundary Line Intercepts" ], "new_concepts": [], "current_concepts": [ "Linear Inequalities", "Boundary Line Intercepts", "Real-world Constraints" ] } ## Find the y-intercept Using the **Boundary Line Intercepts** and **Linear Inequalities** knowledge points $$ \begin{aligned} &4(0) + 2y = 20 \ &2y = 20 \ &y = 10 \end{aligned} $$ ## Find the x-intercept Using the **Boundary Line Intercepts** and **Linear Inequalities** knowledge points $$ \begin{aligned} &4x + 2(0) = 20 \ &4x = 20 \ &x = 5 \end{aligned} $$ Step 1: Identify the $x$- and $y$-intercepts of the boundary line. When $x = 0$, $y =$ 10. When $y = 0$, $x =$ 5. { "elements": [ { "type": "point", "params": [[0, 10]], "properties": { "name": "y-intercept (0, 10)", "size": 4, "color": "#8C55F2", "withLabel": true } }, { "type": "point", "params": [[5, 0]], "properties": { "name": "x-intercept (5, 0)", "size": 4, "color": "#8C55F2", "withLabel": true } }, { "type": "segment", "params": [[0, 10], [5, 0]], "properties": { "strokeColor": "#5583F2", "strokeWidth": 3 } }, { "type": "customzone", "params": [ { "points": [[0, 0], [5, 0], [0, 10]], "fillColor": "rgba(140, 85, 242, 0.3)", "fillOpacity": 0.3 } ] } ], "timestamps": [0.5, 1.0, 1.5] } { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Boundary Line Intercepts" ] }

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Find the y-intercept

Find the x-intercept

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