parallel y-8x-7y=-6

{ "query": { "display": "parallel $$y-8x-7y=-6$$", "symbolab_question": "PRE_CALC#parallel y-8x-7y=-6" }, "solution": { "level": "PERFORMED", "subject": "Functions & Graphing", "topic": "Line Equations", "subTopic": "Parallel", "default": "y=-\\frac{4}{3}x+b", "meta": { "showVerify": true } }, "steps": { "type": "interim", "title": "General line, parallel to $$y-8x-7y=-6:{\\quad}y=-\\frac{4}{3}x+b$$", "steps": [ { "type": "interim", "title": "Find the slope of $$y-8x-7y=-6:{\\quad}m=-\\frac{4}{3}$$", "input": "y-8x-7y=-6", "steps": [ { "type": "interim", "title": "Convert to slope intercept form:$${\\quad}y=-\\frac{4}{3}x+1$$", "input": "y-8x-7y=-6", "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": "step", "primary": "Group like terms", "result": "y-7y-8x=-6" }, { "type": "step", "primary": "Add similar elements: $$y-7y=-6y$$", "result": "-6y-8x=-6" }, { "type": "interim", "title": "Move $$8x\\:$$to the right side", "input": "-6y-8x=-6", "result": "-6y=-6+8x", "steps": [ { "type": "step", "primary": "Add $$8x$$ to both sides", "result": "-6y-8x+8x=-6+8x" }, { "type": "step", "primary": "Simplify", "result": "-6y=-6+8x" } ], "meta": { "interimType": "Move to the Right Title 1Eq", "gptData": "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" } }, { "type": "interim", "title": "Divide both sides by $$-6$$", "input": "-6y=-6+8x", "result": "y=-\\frac{4}{3}x+1", "steps": [ { "type": "step", "primary": "Divide both sides by $$-6$$", "result": "\\frac{-6y}{-6}=-\\frac{6}{-6}+\\frac{8x}{-6}" }, { "type": "step", "primary": "Simplify", "result": "y=-\\frac{4}{3}x+1" } ], "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 equation for the form of $$\\mathbf{y=mx+b}$$, the slope is $$\\mathbf{m}$$", "result": "m=-\\frac{4}{3}" } ], "meta": { "interimType": "Slope Equation Top 1Eq", "gptData": "pG0PljGlka7rWtIVHz2xyoU2cWyPLDgE1QLLHeauuc3PHQdChPJ2JhfqHT+ZU0OMGyxztx1DIZ4Y9QoeLjXWS+siJHKeidrsieDxrGXfcbeBBTEk/JQ2cZ9WKuRzClU7boIj9i72sG3rDqcHqpcq0dfPaQ89/PXC2AOZ/iL7WQVsI5B83GgK4Rq+y4sowjuo" } }, { "type": "interim", "title": "Line with slope m=$$-\\frac{4}{3}:{\\quad}y=-\\frac{4}{3}x+b$$", "steps": [ { "type": "step", "primary": "The slopes of parallel lines are equal" }, { "type": "step", "primary": "Construct the line equation $$\\mathbf{y=mx+b}$$ with $$\\mathbf{m}=-\\frac{4}{3}$$ and a general $$\\mathbf{b}$$", "result": "y=-\\frac{4}{3}x+b" } ], "meta": { "interimType": "Line Equation General 1Eq" } }, { "type": "step", "result": "y=-\\frac{4}{3}x+b" } ], "meta": { "solvingClass": "PreCalc" } }, "meta": { "showVerify": true } }