graph this line using the slope and y-intercept.

\y = 6x + 1\

click to select points on the graph.

Question

graph this line using the slope and y-intercept.

\y = 6x + 1\

click to select points on the graph.

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": true, "concepts_used": [ "Slope-Intercept Form", "Graphing Linear Equations" ], "new_concepts": [], "current_concepts": [ "Slope-Intercept Form", "Graphing Linear Equations" ] } ## Identify the slope and y-intercept Using the *Slope-Intercept Form* knowledge point $$ \begin{aligned} &y = mx + b \ &y = 6x + 1 \implies m = 6,\ b = 1 \end{aligned} $$ ## Plot the y-intercept Using the *Graphing Linear Equations* knowledge point $$ \begin{aligned} &\text{Let } x = 0 \implies y = 1 \ &\text{First point: } (0, 1) \end{aligned} $$ ## Find a second point using the slope Using the *Graphing Linear Equations* knowledge point $$ \begin{aligned} &m = \frac{\Delta y}{\Delta x} = \frac{6}{1} \ &x = 0 + 1 = 1 \ &y = 1 + 6 = 7 \ &\text{Second point: } (1, 7) \end{aligned} $$ To graph the line $y = 6x + 1$, plot the following two points on the coordinate plane: - The $y$-intercept at $(0, 1)$ - A second point at $(1, 7)$ { "elements": [ { "type": "point", "params": [[0, 1]], "properties": { "name": "(0, 1)", "size": 4, "color": "#8C55F2", "withLabel": true } }, { "type": "point", "params": [[1, 7]], "properties": { "name": "(1, 7)", "size": 4, "color": "#8C55F2", "withLabel": true } }, { "type": "line", "params": [[0, 1], [1, 7]], "properties": { "strokeColor": "#5583F2", "strokeWidth": 2 } } ] } { "subject": "Mathematics", "question_type": "Free Response", "knowledge_point": [ "Mathematics", "Geometry", "Graphing Linear Equations" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the slope and y-intercept

Plot the y-intercept

Find a second point using the slope

Answer: