slope of y=2x+1

{ "query": { "display": "slope $$y=2x+1$$", "symbolab_question": "PRE_CALC#slope y=2x+1" }, "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 $$y=2x+1$$", "symbolab_question": "slope y=2x+1" } }, { "method": "Slope using intercept form", "query": { "display": "slopesnd $$y=2x+1$$", "symbolab_question": "slopesnd y=2x+1" } } ], "steps": { "type": "interim", "title": "Slope of $$y=2x+1:{\\quad}m=2$$", "steps": [ { "type": "interim", "title": "Convert to standard form:$${\\quad}2x-y=-1$$", "input": "y=2x+1", "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 $$2x$$ from both sides", "result": "y-2x=2x+1-2x" }, { "type": "step", "primary": "Simplify", "result": "-2x+y=1" }, { "type": "step", "primary": "Multiply both sides by $$-1$$", "result": "-2\\left(-1\\right)x+1\\cdot\\:\\left(-1\\right)y=1\\cdot\\:\\left(-1\\right)" }, { "type": "step", "primary": "Simplify", "result": "2x-y=-1" } ], "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": [ "$$\\mathbf{A}=2,\\:\\mathbf{B}=-1$$" ], "result": "m=-\\frac{2}{-1}" }, { "type": "step", "primary": "Simplify", "result": "m=2" } ], "meta": { "interimType": "Slope Standard Selection 0Eq" } } ], "meta": { "solvingClass": "PreCalc" } }, "meta": { "showVerify": true } }