graph the line with the equation
\y = -x - 3.\

Question

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "explain_then_answer", "quick" ], "needs_drawing": true, "concepts_used": [ "Slope-Intercept Form", "Graphing Linear Equations" ], "new_concepts": [], "current_concepts": [ "Slope-Intercept Form", "Graphing Linear Equations" ] } ## Identify slope and y-intercept $$ \begin{aligned} &y = mx + b \ &y = -x - 3 \ &m = -1, \quad b = -3 \end{aligned} $$ ## Determine key points on the line $$ \begin{aligned} &\text{y-intercept: } (0, -3) \ &\text{For } x = -3: \quad y = -(-3) - 3 = 0 \implies (-3, 0) \ &\text{For } x = 3: \quad y = -(3) - 3 = -6 \implies (3, -6) \end{aligned} $$ To graph the line $y = -x - 3$, plot the $y$-intercept at $(0, -3)$ and use the slope of $-1$ to plot a second point, such as $(1, -4)$ or $(-3, 0)$, then draw a straight line passing through these points. { "elements": [ { "type": "point", "params": [[0, -3]], "properties": { "name": "(0, -3)", "size": 4, "color": "#8C55F2", "withLabel": true } }, { "type": "point", "params": [[-3, 0]], "properties": { "name": "(-3, 0)", "size": 4, "color": "#8C55F2", "withLabel": true } }, { "type": "line", "params": [[0, -3], [-3, 0]], "properties": { "strokeColor": "#8C55F2", "strokeWidth": 3 } } ] } { "subject": "Mathematics", "question_type": "Free Response", "knowledge_point": [ "Mathematics", "Geometry", "Graphing Linear Equations" ] }

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Identify slope and y-intercept

Determine key points on the line

Answer: