8. $y = 4x$

Question

8. $y = 4x$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": true, "concepts_used": [ "Graphing Linear Equations", "Slope-Intercept Form" ], "new_concepts": [], "current_concepts": [ "Graphing Linear Equations", "Slope-Intercept Form", "y-intercept", "Slope Formula" ] } ## Identify the equation form Using the *Slope-Intercept Form* knowledge point $$ \begin{aligned} &y = mx + b\ &y = 4x + 0\ &m = 4,\quad b = 0 \end{aligned} $$ ## Determine key graphing points Using the *Graphing Linear Equations* knowledge point $$ \begin{aligned} &\text{y-intercept: } (0, 0)\ &\text{For } x = 1: y = 4(1) = 4 \implies (1, 4)\ &\text{For } x = -1: y = 4(-1) = -4 \implies (-1, -4) \end{aligned} $$ The equation $y = 4x$ represents a straight line with a slope of $4$ and a $y$-intercept at the origin $(0, 0)$. { "elements": [ { "type": "functiongraph", "params": [ { "js": "4*x", "latex": "y = 4x" }, -10, 10 ], "properties": { "strokeColor": "#8C55F2", "strokeWidth": 3, "name": "y = 4x", "withLabel": true } }, { "type": "point", "params": [ [0, 0] ], "properties": { "name": "(0,0)", "size": 4, "color": "#583C87", "withLabel": true } }, { "type": "point", "params": [ [1, 4] ], "properties": { "name": "(1,4)", "size": 4, "color": "#583C87", "withLabel": true } } ] } { "subject": "Mathematics", "question_type": "Free Response", "knowledge_point": [ "Mathematics", "Geometry", "Graphing Linear Equations" ] }

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Explanation:

Identify the equation form

Determine key graphing points

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