line (-3,-7),(8,-7)

{ "query": { "display": "line $$\\left(-3,\\:-7\\right),\\:\\left(8,\\:-7\\right)$$", "symbolab_question": "PRE_CALC#line (-3,-7),(8,-7)" }, "solution": { "level": "PERFORMED", "subject": "Functions & Graphing", "topic": "Line Equations", "subTopic": "Line", "default": "y=-7", "meta": { "showVerify": true } }, "steps": { "type": "interim", "title": "Line passing through $$\\left(-3,\\:-7\\right)$$, $$\\left(8,\\:-7\\right):{\\quad}y=-7$$", "steps": [ { "type": "step", "primary": "Find the line $$\\mathbf{y=mx+b}$$ passing through $$\\left(-3,\\:-7\\right)$$, $$\\left(8,\\:-7\\right)$$" }, { "type": "interim", "title": "Compute the slope $$\\left(-3,\\:-7\\right),\\:\\left(8,\\:-7\\right):{\\quad}m=0$$", "steps": [ { "type": "step", "primary": "Slope between two points: Slope$$=\\frac{y_2-y_1}{x_2-x_1}$$", "secondary": [ "$$\\left(x_1,\\:y_1\\right)=\\left(-3,\\:-7\\right),\\:\\left(x_2,\\:y_2\\right)=\\left(8,\\:-7\\right)$$" ], "result": "m=\\frac{-7-\\left(-7\\right)}{8-\\left(-3\\right)}" }, { "type": "step", "primary": "Refine", "result": "m=0" } ], "meta": { "interimType": "Slope Two Points Top Level 4Eq" } }, { "type": "interim", "title": "Compute the $$y$$ intercept:$${\\quad}b=-7$$", "steps": [ { "type": "step", "primary": "Plug the slope $$0$$ into $$y=mx+b$$", "result": "y=0\\cdot\\:x+b" }, { "type": "step", "primary": "Plug in $$\\left(-3,\\:-7\\right)$$: $$\\quad\\:x=-3,\\:y=-7$$", "result": "-7=0\\cdot\\:\\left(-3\\right)+b" }, { "type": "step", "primary": "Isolate $$b$$" }, { "type": "interim", "title": "$$-7=0\\cdot\\:\\left(-3\\right)+b{\\quad:\\quad}b=-7$$", "input": "-7=0\\cdot\\:\\left(-3\\right)+b", "steps": [ { "type": "step", "primary": "Switch sides", "result": "0\\cdot\\:\\left(-3\\right)+b=-7" }, { "type": "step", "primary": "Remove parentheses: $$\\left(-a\\right)=-a$$", "result": "-0\\cdot\\:3+b=-7" }, { "type": "step", "primary": "Apply rule $$0\\cdot\\:a=0$$", "result": "-0+b=-7" }, { "type": "step", "primary": "$$-0+b=b$$", "result": "b=-7" } ], "meta": { "solvingClass": "Equations", "interimType": "Equations" } }, { "type": "step", "result": "b=-7" } ], "meta": { "interimType": "Line Equation Find Intersection From Point 0Eq" } }, { "type": "step", "primary": "Construct the line equation $$\\mathbf{y=mx+b}$$ where $$\\mathbf{m}=0$$ and $$\\mathbf{b}=-7$$", "result": "y=-7" } ], "meta": { "solvingClass": "PreCalc" } }, "plot_output": { "meta": { "plotInfo": { "variable": "x", "funcsToDraw": { "funcs": [ { "evalFormula": "y=-7", "displayFormula": "y=-7", "derivativeFormula": "0", "attributes": { "color": "PURPLE", "lineType": "NORMAL", "isAsymptote": false } } ] }, "pointsToDraw": { "pointsLatex": [ "(-3,-7)", "(8,-7)" ], "pointsDecimal": [ { "fst": -3, "snd": -7 }, { "fst": 8, "snd": -7 } ], "attributes": [ { "color": "BLACK", "labels": [ null ], "labelTypes": [ "SOLUTION" ], "labelColors": [ "BLACK" ] }, { "color": "BLACK", "labels": [ null ], "labelTypes": [ "SOLUTION" ], "labelColors": [ "BLACK" ] } ] }, "functionChanges": [ { "origFormulaLatex": [], "finalFormulaLatex": [], "plotTitle": "y=-7", "paramsLatex": [], "paramsReplacementsLatex": [] } ], "localBoundingBox": { "xMin": -10, "xMax": 10.857142857142858, "yMin": -10, "yMax": 10 } }, "showViewLarger": true } }, "meta": { "showVerify": true } }