graph this line using the slope and y-intercept:

\y = x - 2\

click to select points on the graph.

Question

graph this line using the slope and y-intercept:

\y = x - 2\

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 $$ \begin{aligned} &y = mx + b \ &y = 1x - 2 \ &\text{Slope } (m) = 1 \ &\text{y-intercept } (b) = -2 \implies (0, -2) \end{aligned} $$ ## Find a second point on the line Using the *Graphing Linear Equations* knowledge point $$ \begin{aligned} &\text{Rise} = 1,\quad \text{Run} = 1 \ &(x_1, y_1) = (0 + 1, -2 + 1) = (1, -1) \ &(x_2, y_2) = (2, 0) \end{aligned} $$ To graph the line $y = x - 2$, plot the y-intercept at $(0, -2)$ and use the slope of $1$ to plot a second point at $(2, 0)$ or $(1, -1)$, then draw the line passing through them. { "elements": [ { "type": "point", "params": [[0, -2]], "properties": { "name": "y-intercept (0, -2)", "size": 4, "color": "#8C55F2", "withLabel": true } }, { "type": "point", "params": [[2, 0]], "properties": { "name": "x-intercept (2, 0)", "size": 4, "color": "#8C55F2", "withLabel": true } }, { "type": "line", "params": [[0, -2], [2, 0]], "properties": { "strokeColor": "#5583F2", "strokeWidth": 3 } } ] } { "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

Find a second point on the line

Answer: