find an equation for the line that passes through the points $(-2, -1)$ and $(6, 5)$.

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{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": true, "concepts_used": [ "Slope-Intercept Form", "Linear Equations" ], "new_concepts": [], "current_concepts": [ "Slope-Intercept Form", "Linear Equations", "Point-Slope Form" ] } ## Calculate the slope of the line $$ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{5 - (-1)}{6 - (-2)} = \frac{6}{8} = \frac{3}{4} $$ ## Find the y-intercept using point-slope form $$ \begin{aligned} y - y_1 &= m(x - x_1) \ y - 5 &= \frac{3}{4}(x - 6) \ y &= \frac{3}{4}x - \frac{9}{2} + 5 \ y &= \frac{3}{4}x + \frac{1}{2} \end{aligned} $$ Find an equation for the line that passes through the points $(-2, -1)$ and $(6, 5)$. $y = \frac{3}{4}x + \frac{1}{2}$ { "elements": [ { "type": "point", "params": [[-2, -1]], "properties": { "name": "(-2, -1)", "size": 4, "color": "#8C55F2", "withLabel": true } }, { "type": "point", "params": [[6, 5]], "properties": { "name": "(6, 5)", "size": 4, "color": "#8C55F2", "withLabel": true } }, { "type": "functiongraph", "params": [{"js": "0.75*x + 0.5", "latex": "y = \frac{3}{4}x + \frac{1}{2}"}, -10, 10], "properties": { "strokeColor": "#5583F2", "strokeWidth": 2 } } ] } { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Linear Equations" ] }

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Explanation:

Calculate the slope of the line

Find the y-intercept using point-slope form

Answer: