// Numbas version: finer_feedback_settings
{"name": "Determina la ecuaci\u00f3n de la l\u00ednea recta que pasa por los puntos $ A (\\var {a}, \\var {b}) $ y $ B (\\var {c}, \\var {d}) $:  \u00a0", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Determina la ecuaci\u00f3n de la l\u00ednea recta que pasa por los puntos $ A (\\var {a}, \\var {b}) $ y $ B (\\var {c}, \\var {d}) $:  \u00a0", "tags": [], "metadata": {"description": "<p>Encuentra la ecuaci&oacute;n de la l&iacute;nea recta que pasa por los puntos $ (a, b) $ y $ (c, d) $.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "<p><span style=\"vertical-align: inherit;\"><span style=\"vertical-align: inherit;\">Determina la ecuaci&oacute;n de la l&iacute;nea recta que pasa por los puntos $ A (\\var {a}, \\var {b}) $ y $ B (\\var {c}, \\var {d}) $:</span></span></p>\n<p>&nbsp;<br/><span style=\"vertical-align: inherit;\"><span style=\"vertical-align: inherit;\">Ingrese su respuesta en la forma $ mx + c $ para los valores correspondientes de $ m $ y $ c $.</span></span></p>\n<p><strong><span style=\"vertical-align: inherit;\"><span style=\"vertical-align: inherit;\">Indicaci&oacute;n</span></span></strong></p>\n<p><span style=\"vertical-align: inherit;\"><span style=\"vertical-align: inherit;\">Ingrese $ m $ y $ c $ como fracciones o enteros seg&uacute;n sea apropiado y no como decimales.</span></span></p>\n<p><span style=\"vertical-align: inherit;\"><span style=\"vertical-align: inherit;\">Si ingresa $ m $ como fracci&oacute;n, ponga corchetes () alrededor de la fracci&oacute;n. </span><span style=\"vertical-align: inherit;\">Por ejemplo, si su respuesta para $ m $ es $ \\dfrac {-2} {3} $ y su respuesta para $ c $ es $ \\dfrac {7} {5} $, debe escribir $ (- 2/3) x + 7/5 $.</span></span></p>\n<p><span style=\"vertical-align: inherit;\"><span style=\"vertical-align: inherit;\">Haga clic en Mostrar pasos si necesita ayuda</span></span></p>", "advice": "<p>La ecuaci&oacute;n de la recta es de la forma. $y=mx+c$.</p>\n<p>Calcula la pendiente $m=\\dfrac{\\var{d}-(\\var{b})}{\\var{c}-(\\var{a})}=\\dfrac{\\var{d-b}}{\\var{c-a}}$ entre los puntos dados y luego determina el t&eacute;rmino constante $c$ notando que $y=\\var{b}$ cuando $x=\\var{a}$.</p>\n<p>Usando esto obtenemos:<br/>\\[ \\begin{eqnarray} \\var{b}&amp;=&amp;\\simplify[std]{({b-d}/{a-c}){a}+c} \\Rightarrow\\\\ c&amp;=&amp;\\simplify[std]{{b}-({b-d}/{a-c}){a}={(b*c-a*d)}/{(c-a)}} \\end{eqnarray} \\]</p>\n<p>De ah&iacute; que la ecuaci&oacute;n de la recta sea<br/>\\[y = \\simplify[std]{({b-d}/{a-c})x+{b*c-a*d}/{c-a}}\\]</p>", "rulesets": {"std": ["all", "!collectNumbers", "fractionNumbers", "!noLeadingMinus"]}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"d": {"name": "d", "group": "Ungrouped variables", "definition": "random(-9..9)", "description": "", "templateType": "anything", "can_override": false}, "b": {"name": "b", "group": "Ungrouped variables", "definition": "if(b1=d,b1+random(1..3),b1)", "description": "", "templateType": "anything", "can_override": false}, "f": {"name": "f", "group": "Ungrouped variables", "definition": "(b-d)/(a-c)", "description": "", "templateType": "anything", "can_override": false}, "g": {"name": "g", "group": "Ungrouped variables", "definition": "(b*c-a*d)/(c-a)", "description": "", "templateType": "anything", "can_override": false}, "a": {"name": "a", "group": "Ungrouped variables", "definition": "random(1,-1)*random(1..4)", "description": "", "templateType": "anything", "can_override": false}, "c": {"name": "c", "group": "Ungrouped variables", "definition": "a+Random(1..4)*s1", "description": "", "templateType": "anything", "can_override": false}, "b1": {"name": "b1", "group": "Ungrouped variables", "definition": "random(-9..9)", "description": "", "templateType": "anything", "can_override": false}, "s1": {"name": "s1", "group": "Ungrouped variables", "definition": "random(-1,1)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["a", "c", "b", "d", "g", "f", "s1", "b1"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>$y=\\;\\phantom{{}}$[[0]]</p>", "stepsPenalty": 1, "steps": [{"type": "information", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "\n            <p>The equation of the line is of the form $y=mx+c$.</p>\n          <p>Calculate the gradient $m$ between the given points and then calculate the constant term $c$ by noting that $y=\\var{b}$ when $x=\\var{a}$.</p>\n            "}], "gaps": [{"type": "jme", "useCustomName": false, "customName": "", "marks": 2, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "({b-d}/{a-c})x+{b*c-a*d}/{c-a}", "answerSimplification": "std", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "notallowed": {"strings": ["."], "showStrings": false, "partialCredit": 0, "message": "<p>Input all numbers as fractions or integers as appropriate and not as decimals.</p>"}, "valuegenerators": [{"name": "x", "value": ""}]}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "question", "contributors": [{"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}, {"name": "Luis Hernandez", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2870/"}]}]}], "contributors": [{"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}, {"name": "Luis Hernandez", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2870/"}]}