4. a line passes through the points $(-1, 0)$ and $(0, 4)$. 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": [ "Graphing Linear Equations", "x-intercept", "y-intercept" ], "new_concepts": [], "current_concepts": [ "Graphing Linear Equations", "x-intercept", "y-intercept" ] } ## Identify the given intercepts $$ \begin{aligned} &\text{x-intercept: } (-1, 0) \ &\text{y-intercept: } (0, 4) \end{aligned} $$ ## Determine the equation of the line $$ \begin{aligned} &m = \frac{4 - 0}{0 - (-1)} = 4 \ &y = 4x + 4 \end{aligned} $$ ## Plot the points and draw the line $$ \begin{aligned} &\text{Plot } A(-1, 0) \text{ and } B(0, 4) \ &\text{Draw the straight line passing through } A \text{ and } B \end{aligned} $$ To graph the line, plot the points $(-1, 0)$ and $(0, 4)$ on a coordinate plane and draw a straight line passing through both points. The equation of this line is $y = 4x + 4$. { "elements": [ { "type": "point", "params": [[-1, 0]], "properties": { "name": "(-1, 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": [[-1, 0], [0, 4]], "properties": { "strokeColor": "#5583F2", "strokeWidth": 3 } } ] } { "subject": "Mathematics", "question_type": "Free Response", "knowledge_point": [ "Mathematics", "Geometry", "Graphing Linear Equations" ] }

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Explanation:

Identify the given intercepts

Determine the equation of the line

Plot the points and draw the line

Answer: