3. a line has an $x$-intercept of 2 and a $y$-intercept of $-5$. graph the line.

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{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "explain_then_answer", "quick" ], "needs_drawing": true, "concepts_used": [ "x-intercept", "y-intercept" ], "new_concepts": [ "Graphing Linear Equations" ], "current_concepts": [ "x-intercept", "y-intercept", "Graphing Linear Equations" ] } ## Identify the coordinates of the intercepts $$ \begin{aligned} &\text{x-intercept} = 2 \implies (2, 0) \ &\text{y-intercept} = -5 \implies (0, -5) \end{aligned} $$ ## Determine the equation of the line $$ \begin{aligned} &m = \frac{-5 - 0}{0 - 2} = \frac{5}{2} \ &y = \frac{5}{2}x - 5 \end{aligned} $$ ## Plot the points and draw the line $$ \text{Plot } (2, 0) \text{ and } (0, -5) \text{ on the coordinate plane and draw a straight line through them.} $$ To graph the line, plot the points corresponding to the intercepts and draw a straight line through them: * **$x$-intercept of 2:** Plot the point $(2, 0)$ on the $x$-axis. * **$y$-intercept of $-5$:** Plot the point $(0, -5)$ on the $y$-axis. { "elements": [ { "type": "point", "params": [[2, 0]], "properties": { "name": "(2, 0)", "size": 4, "color": "#8C55F2", "withLabel": true } }, { "type": "point", "params": [[0, -5]], "properties": { "name": "(0, -5)", "size": 4, "color": "#8C55F2", "withLabel": true } }, { "type": "line", "params": [[2, 0], [0, -5]], "properties": { "strokeColor": "#5583F2", "strokeWidth": 3 } } ], "timestamps": [0.5, 1.0, 1.5] } { "subject": "Mathematics", "question_type": "Free Response", "knowledge_point": [ "Mathematics", "Geometry", "Graphing Linear Equations" ] }

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Explanation:

Identify the coordinates of the intercepts

Determine the equation of the line

Plot the points and draw the line

Answer: