4. use the points (0, 4) and (-2, 3) to find the slope of the line and give the equation of this line.

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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 Formula", "Slope-Intercept Form" ], "new_concepts": [], "current_concepts": [ "Slope Formula", "Slope-Intercept Form", "Equation of a Line" ] } ## Calculate the slope of the line Using the *Slope Formula* knowledge point $$ \begin{aligned} &(x_1, y_1) = (0, 4),\quad (x_2, y_2) = (-2, 3)\ &m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{3 - 4}{-2 - 0} = \frac{-1}{-2} = \frac{1}{2} \end{aligned} $$ ## Determine the equation of the line Using the *Slope-Intercept Form* knowledge point $$ \begin{aligned} &y = mx + b\ &\text{Since } (0, 4) \text{ is the } y\text{-intercept, } b = 4\ &y = \frac{1}{2}x + 4 \end{aligned} $$ Slope: $\frac{1}{2}$ Equation of the line: $y = \frac{1}{2}x + 4$ { "elements": [ { "type": "point", "params": [[0, 4]], "properties": { "name": "(0, 4)", "size": 4, "color": "#8C55F2", "withLabel": true } }, { "type": "point", "params": [[-2, 3]], "properties": { "name": "(-2, 3)", "size": 4, "color": "#8C55F2", "withLabel": true } }, { "type": "functiongraph", "params": [{"js": "0.5*x + 4", "latex": "y = \frac{1}{2}x + 4"}, -10, 10], "properties": { "strokeColor": "#5583F2", "strokeWidth": 2 } } ] } { "subject": "Mathematics", "question_type": "Free Response", "knowledge_point": [ "Mathematics", "Geometry", "Equation of a Line" ] }

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Calculate the slope of the line

Determine the equation of the line

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