slope of y=-2/3 x+4

{ "query": { "display": "slope $$y=-\\frac{2}{3}x+4$$", "symbolab_question": "PRE_CALC#slope y=-\\frac{2}{3}x+4" }, "solution": { "level": "PERFORMED", "subject": "Functions & Graphing", "topic": "Line Equations", "subTopic": "Slope", "default": "m=-\\frac{2}{3}", "meta": { "showVerify": true } }, "methods": [ { "method": "Slope using standard form", "query": { "display": "slope $$y=-\\frac{2}{3}x+4$$", "symbolab_question": "slope y=-\\frac{2}{3}x+4" } }, { "method": "Slope using intercept form", "query": { "display": "slopesnd $$y=-\\frac{2}{3}x+4$$", "symbolab_question": "slopesnd y=-\\frac{2}{3}x+4" } } ], "steps": { "type": "interim", "title": "Slope of $$y=-\\frac{2}{3}x+4:{\\quad}m=-\\frac{2}{3}$$", "steps": [ { "type": "interim", "title": "Convert to standard form:$${\\quad}2x+3y=12$$", "input": "y=-\\frac{2}{3}x+4", "steps": [ { "type": "definition", "title": "Standard form definition", "text": "$$\\mathbf{Ax+By=C}\\:$$is the standard form of a line, $$\\mathbf{A}\\:$$is positive integer, $$\\mathbf{B},\\:\\mathbf{C}\\:$$are integers" }, { "type": "step", "primary": "Add $$\\frac{2}{3}x$$ to both sides", "result": "y+\\frac{2}{3}x=-\\frac{2}{3}x+4+\\frac{2}{3}x" }, { "type": "step", "primary": "Simplify", "result": "\\frac{2}{3}x+y=4" }, { "type": "step", "primary": "Multiply both sides by $$3$$", "result": "\\frac{2}{3}\\cdot\\:3x+1\\cdot\\:3y=4\\cdot\\:3" }, { "type": "step", "primary": "Simplify", "result": "2x+3y=12" } ], "meta": { "interimType": "Convert To Standard Linear Equation 0Eq" } }, { "type": "interim", "title": "Slope using standard form:$${\\quad}m=-\\frac{2}{3}$$", "result": "m=-\\frac{2}{3}", "steps": [ { "type": "step", "primary": "Slope $$\\mathbf{m}\\:$$of a line of the form $$\\mathbf{Ax+By=C}\\:$$equals $$\\mathbf{-\\frac{A}{B}}$$", "secondary": [ "$$\\mathbf{A}=2,\\:\\mathbf{B}=3$$" ], "result": "m=-\\frac{2}{3}" } ], "meta": { "interimType": "Slope Standard Selection 0Eq" } } ], "meta": { "solvingClass": "PreCalc" } }, "meta": { "showVerify": true } }