slope ofintercept 3x-2y=-11

{ "query": { "display": "slope intercept $$3x-2y=-11$$", "symbolab_question": "PRE_CALC#slopeintercept 3x-2y=-11" }, "solution": { "level": "PERFORMED", "subject": "Functions & Graphing", "topic": "Line Equations", "subTopic": "Slope Intercept", "default": "y=\\frac{3}{2}x+\\frac{11}{2}" }, "steps": { "type": "interim", "title": "Slope-Intercept form of $$3x-2y=-11:{\\quad}y=\\frac{3}{2}x+\\frac{11}{2}$$", "input": "3x-2y=-11", "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:$${\\quad}y=\\frac{3}{2}x+\\frac{11}{2}$$", "input": "3x-2y=-11", "steps": [ { "type": "interim", "title": "Move $$3x\\:$$to the right side", "input": "3x-2y=-11", "result": "-2y=-11-3x", "steps": [ { "type": "step", "primary": "Subtract $$3x$$ from both sides", "result": "3x-2y-3x=-11-3x" }, { "type": "step", "primary": "Simplify", "result": "-2y=-11-3x" } ], "meta": { "interimType": "Move to the Right Title 1Eq", "gptData": "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" } }, { "type": "interim", "title": "Divide both sides by $$-2$$", "input": "-2y=-11-3x", "result": "y=\\frac{3}{2}x+\\frac{11}{2}", "steps": [ { "type": "step", "primary": "Divide both sides by $$-2$$", "result": "\\frac{-2y}{-2}=-\\frac{11}{-2}-\\frac{3x}{-2}" }, { "type": "step", "primary": "Simplify", "result": "y=\\frac{3}{2}x+\\frac{11}{2}" } ], "meta": { "interimType": "Divide Both Sides Specific 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{3}{2}x+\\frac{11}{2}" } ], "meta": { "solvingClass": "PreCalc" } } }