slope of-4x+7=2y-3

{ "query": { "display": "slope $$-4x+7=2y-3$$", "symbolab_question": "PRE_CALC#slope -4x+7=2y-3" }, "solution": { "level": "PERFORMED", "subject": "Functions & Graphing", "topic": "Line Equations", "subTopic": "Slope", "default": "m=-2", "meta": { "showVerify": true } }, "methods": [ { "method": "Slope using standard form", "query": { "display": "slope $$-4x+7=2y-3$$", "symbolab_question": "slope -4x+7=2y-3" } }, { "method": "Slope using intercept form", "query": { "display": "slopesnd $$-4x+7=2y-3$$", "symbolab_question": "slopesnd -4x+7=2y-3" } } ], "steps": { "type": "interim", "title": "Slope of $$-4x+7=2y-3:{\\quad}m=-2$$", "steps": [ { "type": "interim", "title": "Convert to standard form:$${\\quad}4x+2y=10$$", "input": "-4x+7=2y-3", "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": "Subtract $$7$$ from both sides", "result": "-4x+7-7=2y-3-7" }, { "type": "step", "primary": "Simplify", "result": "-4x=2y-10" }, { "type": "step", "primary": "Subtract $$2y$$ from both sides", "result": "-4x-2y=2y-10-2y" }, { "type": "step", "primary": "Simplify", "result": "-4x-2y=-10" }, { "type": "step", "primary": "Multiply both sides by $$-1$$", "result": "-4\\left(-1\\right)x-2\\left(-1\\right)y=-10\\left(-1\\right)" }, { "type": "step", "primary": "Simplify", "result": "4x+2y=10" } ], "meta": { "interimType": "Convert To Standard Linear Equation 0Eq" } }, { "type": "interim", "title": "Slope using standard form:$${\\quad}m=-2$$", "result": "m=-2", "steps": [ { "type": "step", "primary": "Slope $$\\mathbf{m}\\:$$of a line of the form $$\\mathbf{Ax+By=C}\\:$$equals $$\\mathbf{-\\frac{A}{B}}$$", "secondary": [ "$$\\mathbf{A}=4,\\:\\mathbf{B}=2$$" ], "result": "m=-\\frac{4}{2}" }, { "type": "step", "primary": "Simplify", "result": "m=-2" } ], "meta": { "interimType": "Slope Standard Selection 0Eq" } } ], "meta": { "solvingClass": "PreCalc" } }, "meta": { "showVerify": true } }