graph the line whose $x$-intercept is 6 and whose $y$-intercept is 4.

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{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": true, "concepts_used": [ "Coordinate Plotting", "Graphing Linear Equations" ], "new_concepts": [ "Intercepts" ], "current_concepts": [ "Coordinate Plotting", "Graphing Linear Equations", "Intercepts" ] } ## Identify the coordinates of the intercepts Using the *Coordinate Plotting* knowledge point $$ \begin{aligned} &\text{x-intercept is } 6 \implies (6, 0)\ &\text{y-intercept is } 4 \implies (0, 4) \end{aligned} $$ ## Plot the points and draw the line Using the *Graphing Linear Equations* knowledge point $$ \begin{aligned} &\text{Plot } (6, 0) \text{ on the x-axis.}\ &\text{Plot } (0, 4) \text{ on the y-axis.}\ &\text{Draw a straight line passing through both points.} \end{aligned} $$ To graph the line, plot the point $(6, 0)$ on the x-axis and the point $(0, 4)$ on the y-axis, then draw a straight line passing through both points. { "elements": [ { "type": "point", "params": [[6, 0]], "properties": { "name": "(6,0)", "size": 4, "color": "#8C55F2", "withLabel": true } }, { "type": "point", "params": [[0, 4]], "properties": { "name": "(0,4)", "size": 4, "color": "#8C55F2", "withLabel": true } }, { "type": "line", "params": [[6, 0], [0, 4]], "properties": { "strokeColor": "#5583F2", "strokeWidth": 3 } } ] } { "subject": "Mathematics", "question_type": "Free Response", "knowledge_point": [ "Mathematics", "Geometry", "Coordinate Plotting" ] }

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Explanation:

Identify the coordinates of the intercepts

Plot the points and draw the line

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