line 7x-8y=0

{ "query": { "display": "line $$7x-8y=0$$", "symbolab_question": "PRE_CALC#line 7x-8y=0" }, "solution": { "level": "PERFORMED", "subject": "Functions & Graphing", "topic": "Line Equations", "subTopic": "Line", "default": "y=\\frac{7}{8}x", "meta": { "showVerify": true } }, "steps": { "type": "interim", "title": "Line $$7x-8y=0$$: slope m=$$\\frac{7}{8}\\:$$and intercept b=$$0$$", "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:$${\\quad}y=\\frac{7}{8}x$$", "input": "7x-8y=0", "steps": [ { "type": "interim", "title": "Move $$7x\\:$$to the right side", "input": "7x-8y=0", "result": "-8y=-7x", "steps": [ { "type": "step", "primary": "Subtract $$7x$$ from both sides", "result": "7x-8y-7x=0-7x" }, { "type": "step", "primary": "Simplify", "result": "-8y=-7x" } ], "meta": { "interimType": "Move to the Right Title 1Eq", "gptData": "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" } }, { "type": "interim", "title": "Divide both sides by $$-8$$", "input": "-8y=-7x", "result": "y=\\frac{7}{8}x", "steps": [ { "type": "step", "primary": "Divide both sides by $$-8$$", "result": "\\frac{-8y}{-8}=\\frac{-7x}{-8}" }, { "type": "step", "primary": "Simplify", "result": "y=\\frac{7}{8}x" } ], "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{7}{8}x+0" } ], "meta": { "solvingClass": "PreCalc" } }, "plot_output": { "meta": { "plotInfo": { "variable": "x", "funcsToDraw": { "funcs": [ { "evalFormula": "y=\\frac{7x}{8}", "displayFormula": "y=\\frac{7}{8}x", "derivativeFormula": "\\frac{7}{8}", "attributes": { "color": "PURPLE", "lineType": "NORMAL", "isAsymptote": false } } ] }, "functionChanges": [ { "origFormulaLatex": [ "\\frac{7}{8}x" ], "finalFormulaLatex": [ "\\frac{7x}{8}" ], "plotTitle": "y=\\frac{7}{8}x", "paramsLatex": [], "paramsReplacementsLatex": [] } ], "localBoundingBox": { "xMin": -12.239999999999998, "xMax": 12.239999999999998, "yMin": -7.5600000000000005, "yMax": 7.5600000000000005 } }, "showViewLarger": true } }, "meta": { "showVerify": true } }