line y-2=-2/3 (x-4)

{ "query": { "display": "line $$y-2=-\\frac{2}{3}\\left(x-4\\right)$$", "symbolab_question": "PRE_CALC#line y-2=-\\frac{2}{3}(x-4)" }, "solution": { "level": "PERFORMED", "subject": "Functions & Graphing", "topic": "Line Equations", "subTopic": "Line", "default": "y=-\\frac{2}{3}x+\\frac{14}{3}", "meta": { "showVerify": true } }, "steps": { "type": "interim", "title": "Line $$y-2=-\\frac{2}{3}\\left(x-4\\right)$$: slope m=$$-\\frac{2}{3}\\:$$and intercept b=$$\\frac{14}{3}$$", "steps": [ { "type": "definition", "title": "Slope intercept form defininition", "text": "$$\\mathbf{y=mx+b}\\:$$is the slope intercept form of a line where $$\\mathbf{m}\\:$$is the slope and $$\\mathbf{b}\\:$$is the $$\\mathbf{y}\\:$$intercept" }, { "type": "interim", "title": "Convert to slope intercept form:$${\\quad}y=-\\frac{2}{3}x+\\frac{14}{3}$$", "input": "y-2=-\\frac{2}{3}\\left(x-4\\right)", "steps": [ { "type": "interim", "title": "Move $$2\\:$$to the right side", "input": "y-2=-\\frac{2}{3}\\left(x-4\\right)", "result": "y=-\\frac{2}{3}x+\\frac{14}{3}", "steps": [ { "type": "step", "primary": "Add $$2$$ to both sides", "result": "y-2+2=-\\frac{2}{3}\\left(x-4\\right)+2" }, { "type": "step", "primary": "Simplify", "result": "y=-\\frac{2}{3}x+\\frac{14}{3}" } ], "meta": { "interimType": "Move to the Right Title 1Eq", "gptData": "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" } } ], "meta": { "interimType": "Convert To Intercept Linear Equation 0Eq" } }, { "type": "step", "primary": "For a line in the form of $$\\mathbf{y=mx+b}$$, the slope is $$\\mathbf{m}\\:$$and $$\\mathbf{y}\\:$$intercept is $$\\mathbf{b}$$", "result": "y=-\\frac{2}{3}x+\\frac{14}{3}" } ], "meta": { "solvingClass": "PreCalc" } }, "plot_output": { "meta": { "plotInfo": { "variable": "x", "funcsToDraw": { "funcs": [ { "evalFormula": "y=\\frac{-2x+14}{3}", "displayFormula": "y=-\\frac{2}{3}x+\\frac{14}{3}", "derivativeFormula": "-\\frac{2}{3}", "attributes": { "color": "PURPLE", "lineType": "NORMAL", "isAsymptote": false } } ] }, "functionChanges": [ { "origFormulaLatex": [ "-\\frac{2}{3}x+\\frac{14}{3}" ], "finalFormulaLatex": [ "\\frac{-2x+14}{3}" ], "plotTitle": "y=-\\frac{2}{3}x+\\frac{14}{3}", "paramsLatex": [], "paramsReplacementsLatex": [] } ], "localBoundingBox": { "xMin": -20.412, "xMax": 26.711999999999996, "yMin": -9.112133333333333, "yMax": 13.265466666666665 } }, "showViewLarger": true } }, "meta": { "showVerify": true } }