graph the line.

$y = 2x + 3$

Question

graph the line.

$y = 2x + 3$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "explain_then_answer", "quick" ], "needs_drawing": true, "concepts_used": [ "Graphing Linear Equations", "Slope-Intercept Form" ], "new_concepts": [], "current_concepts": [ "Graphing Linear Equations", "Slope-Intercept Form", "Coordinate Plotting" ] } ## Identify the y-intercept $$ \begin{aligned} &\text{Equation: } y = 2x + 3\ &\text{Form: } y = mx + b\ &b = 3 \implies (0, 3) \end{aligned} $$ ## Find a second point using the slope $$ \begin{aligned} &m = 2 = \frac{\text{rise}}{\text{run}} = \frac{2}{1}\ &x_2 = 0 + 1 = 1\ &y_2 = 3 + 2 = 5 \implies (1, 5) \end{aligned} $$ ## Verify with another point $$ \begin{aligned} &x = -1\ &y = 2(-1) + 3 = 1 \implies (-1, 1) \end{aligned} $$ To graph the line $y = 2x + 3$, plot the y-intercept at $(0, 3)$ and use the slope of $2$ to plot a second point at $(1, 5)$ or $(-1, 1)$, then draw a straight line passing through these points. { "elements": [ { "type": "point", "params": [[0, 3]], "properties": { "name": "y-intercept (0, 3)", "size": 4, "color": "#8C55F2", "withLabel": true } }, { "type": "point", "params": [[1, 5]], "properties": { "name": "(1, 5)", "size": 4, "color": "#8C55F2", "withLabel": true } }, { "type": "line", "params": [[0, 3], [1, 5]], "properties": { "strokeColor": "#5583F2", "strokeWidth": 3 } } ] } { "subject": "Mathematics", "question_type": "Free Response", "knowledge_point": [ "Mathematics", "Geometry", "Graphing Linear Equations" ] }

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Question

Explanation:

Identify the y-intercept

Find a second point using the slope

Verify with another point

Answer: