slope of y= 3/2 x+2

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