the graph below represents the linear equation $y = \frac{1}{2}x - 3$.

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{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": true, "concepts_used": [ "Slope-Intercept Form" ], "new_concepts": [ "Linear Equation Graphing" ], "current_concepts": [ "Slope-Intercept Form", "Linear Equation Graphing" ] } ## Identify the given linear equation Using the *Slope-Intercept Form* knowledge point $$ y = \frac{1}{2}x - 3 $$ ## Determine the y-intercept Using the *Slope-Intercept Form* knowledge point $$ \begin{aligned} &y = mx + b \ &b = -3 \implies (0, -3) \end{aligned} $$ ## Determine the slope and a second point Using the *Slope-Intercept Form* knowledge point $$ \begin{aligned} &m = \frac{\text{rise}}{\text{run}} = \frac{1}{2} \ &(0 + 2, -3 + 1) = (2, -2) \ &(6, 0) \quad \text{is the x-intercept} \end{aligned} $$ The graph represents the linear equation $y = \frac{1}{2}x - 3$, which has a $y$-intercept at $(0, -3)$, a slope of $\frac{1}{2}$, and an $x$-intercept at $(6, 0)$. { "elements": [ { "type": "point", "params": [[0, -3]], "properties": { "name": "y-intercept (0, -3)", "size": 4, "color": "#8C55F2", "withLabel": true } }, { "type": "point", "params": [[6, 0]], "properties": { "name": "x-intercept (6, 0)", "size": 4, "color": "#8C55F2", "withLabel": true } }, { "type": "line", "params": [[0, -3], [6, 0]], "properties": { "strokeColor": "#5583F2", "strokeWidth": 3 } } ] } { "subject": "Mathematics", "question_type": "Free Response", "knowledge_point": [ "Mathematics", "Algebra", "Slope-Intercept Form" ] }

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Explanation:

Identify the given linear equation

Determine the y-intercept

Determine the slope and a second point

Answer: