// Numbas version: exam_results_page_options
{"name": "Dadas las ecuaciones de rectas paralelas....", "extensions": ["geogebra"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Dadas las ecuaciones de rectas paralelas....", "tags": [], "metadata": {"description": "", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "<p>Considera las rectas: $ A_0 $ , $B_0$, $C_0$ y $E_0 $ que aparecen en el gr&aacute;fico y usa estas ecuaciones para decidir cuales son paralelas.</p>\n<p>{geogebra_applet('WuavQqEG',[[\"m1\",m1],[\"m2\",m2],[\"m3\",m3],[\"c1\",c1],[\"c2\",c2],[\"c3\",c3],[\"c4\",c4],[\"c5\",c5],[\"f1\",f1],[\"d1\",d1],[\"a1\",a1],[\"b1\",b1]])}</p>", "advice": "<h4>a)</h4>\n<p>Parallel lines are&nbsp;defined as lines that remain<strong> the same</strong> distance apart and so they never meet. This means that their&nbsp;<strong>gradient</strong> is the same.</p>\n<p>If we write our line equations in the form $y_i=m_i\\times x_i+c_i$, then for parallel lines,&nbsp;<strong>$m_1=m_2$</strong>.</p>\n<p>Vertical lines are always parallel to <strong>the $y$-axis</strong> and horizontal lines are always parallel to <strong>the $x$-axis</strong>.</p>\n<h4>b)</h4>\n<p>All but one of the straight lines above follow the general formula $y=mx+c$ where $m$ is a constant denoting the gradient of the line and $c$ is a constant denoting the $y$-intercept of the line.&nbsp;</p>\n<p>The gradient (given by $m$), indicates the slope of a straight line. Where this&nbsp;is positive, the $y$-coordinate along the line increases by $m$ for every increase in the value of $x$ by $1$. For example, $y=3x$ indicates that for every increase in the value of $x$ by $1$, the value of $y$ increases by $3$. Where there is no $m$ (i.e. $y=c$), the line is horizontal as the value of $y$ has no dependence on the value of $x$.</p>\n<p>The $y$-intercept (given by $c$), indicates the point where the line passes through the $y$-axis. If the line equation has no $c$ (i.e. $y=mx$), the line has a $y$ intercept of $0$ (passing through the origin).</p>\n<p>We can use our knowledge of the slope of the line and the $y$-intercept to then judge which points on the graph correspond to which equations.</p>\n<p><strong>A:</strong></p>\n<p>$y=\\simplify{{m1}x+{c1}}$ &nbsp;gives us $m=\\var{m1}$ and $c=\\var{c1}$.</p>\n<p><strong>B:</strong></p>\n<p>$y=\\simplify{{m2}x+{c2}}$ &nbsp;gives us $m=\\var{m2}$ and $c=\\var{c2}$.</p>\n<p><strong>C:</strong></p>\n<p>$y=\\simplify{{m3}x+{c3}}$ &nbsp;gives us $m=\\var{m3}$ and $c=\\var{c3}$.</p>\n<p><strong>D:</strong></p>\n<p>$y=\\simplify{{c4}}$ &nbsp;gives us $m=0$ and $c=\\var{c1}$.</p>\n<p><strong>E:</strong></p>\n<p>$x=\\var{c5}$ &nbsp;is the exception to the $y=mx+c$ form of writing straight line equations. This equation gives a value for $x$ independent of the value of $y$, so a vertical line is formed at the $x$-coordinate $\\var{c5}$.</p>\n<h4>c)</h4>\n<p>For the equation&nbsp;$y=\\var{cfake}$, the gradient is $0$, so we check our lines $A_0, B_0, C_0, D_0 \\text{ and }E_0$ to find $D_0$ has the same gradient. Therefore $D_0$ is parallel to $y=\\var{cfake}$.</p>\n<h4>d)</h4>\n<p>For the equation $y=\\var{m1}x+\\var{cpar}$, the gradient is $\\var{m1}$, so we check our lines $A_0, B_0, C_0, D_0 \\text{ and }E_0$ to find both $A_0$ and $B_0$ have the same gradient. Therefore $A_0$ and $B_0$ are&nbsp;parallel to $y=\\var{m1}x+\\var{cpar}$.</p>\n<h4>e)</h4>\n<p>This time, we have to find the gradient of the $x$-axis. Note that the $x$-axis is equivalent to the line with equation $y=0$. The gradient of this line is $0$, so we check our lines $A_0, B_0, C_0, D_0 \\text{ and }E_0$ to find $D_0$ has the same gradient. Therefore $D_0$ is parallel to $y=0$ and in other words, $D_0$ is parallel to the $x$-axis.</p>\n<h4>f)</h4>\n<p>For the equation $y=\\simplify{{muniq}x+{c1}}$, the gradient is $\\var{muniq}$, so we check our lines $A_0, B_0, C_0, D_0 \\text{ and }E_0$ to find none have the same gradient. Therefore none of the labelled lines are&nbsp;parallel to $y=\\simplify{{muniq}x+{c1}}$.</p>\n<h4>g)</h4>\n<p>Lines that are parallel have the same gradient. This is represented by $m$ in the general form of a straight line ($y=mx+c$). The gradient of $C_0$ was $\\var{m3}$, so any straight line parallel to $C_0$ will share this value for $m$.</p>\n<p>Therefore, we input $y=\\var{m3}x+c$.</p>", "rulesets": {}, "extensions": ["geogebra"], "variables": {"m1": {"name": "m1", "group": "Gradient", "definition": "random(1..2#0.1)", "description": "", "templateType": "anything"}, "b1": {"name": "b1", "group": "Point variables(removed)", "definition": "25", "description": "", "templateType": "anything"}, "a1": {"name": "a1", "group": "Point variables(removed)", "definition": "30", "description": "", "templateType": "anything"}, "c4": {"name": "c4", "group": "intercept", "definition": "random(3..6)", "description": "", "templateType": "anything"}, "c3": {"name": "c3", "group": "intercept", "definition": "random(1..5)", "description": "", "templateType": "anything"}, "cfake": {"name": "cfake", "group": "intercept", "definition": "random(-8..-3)", "description": "", "templateType": "anything"}, "c5": {"name": "c5", "group": "intercept", "definition": "random(14..17)", "description": "", "templateType": "anything"}, "d1": {"name": "d1", "group": "Point variables(removed)", "definition": "60", "description": "", "templateType": "anything"}, "c1": {"name": "c1", "group": "intercept", "definition": "random(-10..-5)", "description": "", "templateType": "anything"}, "mfake": {"name": "mfake", "group": "Gradient", "definition": "random(-4..-1)", "description": "", "templateType": "anything"}, "c10": {"name": "c10", "group": "Point variables(removed)", "definition": "-30/m3", "description": "", "templateType": "anything"}, "c2": {"name": "c2", "group": "intercept", "definition": "random(15..20)", "description": "", "templateType": "anything"}, "m2": {"name": "m2", "group": "Gradient", "definition": "m1", "description": "", "templateType": "anything"}, "f1": {"name": "f1", "group": "Point variables(removed)", "definition": "-40", "description": "", "templateType": "anything"}, "m3": {"name": "m3", "group": "Gradient", "definition": "random(-2..-1#0.1)", "description": "", "templateType": "anything"}, "muniq": {"name": "muniq", "group": "Gradient", "definition": "random(10..50 except m1 m2 m3 mfake)", "description": "", "templateType": "anything"}, "cpar": {"name": "cpar", "group": "intercept", "definition": "random(500..750)", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": [], "variable_groups": [{"name": "Gradient", "variables": ["m1", "m2", "m3", "mfake", "muniq"]}, {"name": "intercept", "variables": ["c1", "c2", "c3", "c4", "c5", "cfake", "cpar"]}, {"name": "Point variables(removed)", "variables": ["a1", "b1", "c10", "d1", "f1"]}], "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>A continuaci&oacute;n complete los espacios para la descripci&oacute;n de las rectas paralelas.</p>\n<p>Las rectas paralelas se definen como rectas que permanecen [[0]]&nbsp;distancia&nbsp; y nunca se encuentran. Esto significa que su [[1]]&nbsp;es la misma.</p>\n<p>Si escribimos las ecuaciones de la recta en la forma. $y=m_i\\cdot x_i+c_i$, entonces las rectas paralelas tienen:&nbsp;[[2]] $=$&nbsp;[[3]].</p>\n<p>Las rectas verticales son siempre paralelas al&nbsp;[[4]]&nbsp;y las rectas horizontales son siempre paralelas&nbsp; al&nbsp;[[5]].</p>", "gaps": [{"type": "1_n_2", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minMarks": 0, "maxMarks": 0, "shuffleChoices": true, "displayType": "dropdownlist", "displayColumns": 0, "showCellAnswerState": true, "choices": ["A igual&nbsp;", "<p>a una variable</p>", "<p>2 unidades de&nbsp;</p>"], "matrix": ["1", 0, 0], "distractors": ["", "", ""]}, {"type": "1_n_2", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minMarks": 0, "maxMarks": 0, "shuffleChoices": true, "displayType": "dropdownlist", "displayColumns": 0, "showCellAnswerState": true, "choices": ["pendiente", "<p>intersecci&oacute;n en el eje $y$</p>", "<p>longitud</p>", "<p>color</p>", "<p>Intersecci&oacute;n en el eje $x$</p>"], "matrix": ["1", 0, 0, 0, 0], "distractors": ["", "", "", "", ""]}, {"type": "1_n_2", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minMarks": 0, "maxMarks": 0, "shuffleChoices": false, "displayType": "dropdownlist", "displayColumns": 0, "showCellAnswerState": true, "choices": ["<p>m\u2081</p>", "<p>c\u2081</p>", "<p>x\u2081</p>", "<p>y\u2081</p>"], "matrix": ["1", 0, 0, 0], "distractors": ["", "", "", ""]}, {"type": "1_n_2", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minMarks": 0, "maxMarks": 0, "shuffleChoices": false, "displayType": "dropdownlist", "displayColumns": 0, "showCellAnswerState": true, "choices": ["<p>m\u2082</p>", "<p>c\u2082</p>", "<p>x\u2082</p>", "<p>y\u2082</p>"], "matrix": ["1", 0, 0, 0], "distractors": ["", "", "", ""]}, {"type": "1_n_2", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minMarks": 0, "maxMarks": 0, "shuffleChoices": false, "displayType": "dropdownlist", "displayColumns": 0, "showCellAnswerState": true, "choices": ["<p>al eje x</p>", "<p>al eje y</p>", "<p>y=x</p>", "ninguna"], "matrix": ["0", "1", 0, 0], "distractors": ["", "", "", ""]}, {"type": "1_n_2", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minMarks": 0, "maxMarks": 0, "shuffleChoices": false, "displayType": "dropdownlist", "displayColumns": 0, "showCellAnswerState": true, "choices": ["<p>al eje x</p>", "<p>al eje y</p>", "<p>y=x</p>", "ninguna"], "matrix": ["1", 0, 0, 0], "distractors": ["", "", "", ""]}], "sortAnswers": false}, {"type": "m_n_x", "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>Usa el gr&aacute;fico de arriba para hacer coincidir la recta con su respectiva ecuaci&oacute;n.</p>", "minMarks": 0, "maxMarks": 0, "minAnswers": 0, "maxAnswers": 0, "shuffleChoices": true, "shuffleAnswers": false, "displayType": "radiogroup", "warningType": "none", "showCellAnswerState": true, "choices": ["<p>$y=\\simplify{{m1}x+{c1}}$</p>", "<p>$y=\\simplify{{m2}x+{c2}}$</p>", "<p>$y=\\simplify{{m3}x+{c3}}$</p>", "<p>$y=\\var{c4}$</p>", "<p>$x=\\var{c5}$</p>", "<p>$y=\\simplify{{mfake}x+{cfake}}$</p>"], "matrix": [["1", 0, 0, 0, 0, 0], [0, "1", 0, 0, 0, 0], [0, 0, "1", 0, 0, 0], [0, 0, 0, "1", 0, 0], [0, 0, 0, 0, "1", 0], [0, 0, 0, 0, 0, "1"]], "layout": {"type": "all", "expression": ""}, "answers": ["<p>$A_0$</p>", "<p>$B_0$</p>", "<p>$C_0$</p>", "<p>$D_0$</p>", "<p>$E_0$</p>", "Ninguna de estas"]}, {"type": "m_n_2", "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>&iquest;Qu&eacute; rectas son paralelas a la recta con ecuaci&oacute;n $y=\\var{cfake}$?</p>", "minMarks": 0, "maxMarks": 0, "shuffleChoices": false, "displayType": "checkbox", "displayColumns": 0, "minAnswers": 0, "maxAnswers": 0, "warningType": "none", "showCellAnswerState": true, "choices": ["<p>$A_0$</p>", "<p>$B_0$</p>", "<p>$C_0$</p>", "<p>$D_0$</p>", "<p>$E_0$</p>", "<p>Ninguna de estas</p>"], "matrix": [0, 0, 0, "1", 0, 0], "distractors": ["", "", "", "", "", ""]}, {"type": "m_n_2", "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>&iquest;Qu&eacute; rectas son paralelas a la recta con ecuaci&oacute;n $y=\\var{m1}x+\\var{cpar}$?</p>", "minMarks": "0", "maxMarks": "1", "shuffleChoices": false, "displayType": "checkbox", "displayColumns": 0, "minAnswers": 0, "maxAnswers": 0, "warningType": "none", "showCellAnswerState": true, "choices": ["<p>$A_0$</p>", "<p>$B_0$</p>", "<p>$C_0$</p>", "<p>$D_0$</p>", "<p>$E_0$</p>", "<p>Ninguna de estas</p>"], "matrix": ["1/2", "1/2", 0, "0", 0, 0], "distractors": ["", "", "", "", "", ""]}, {"type": "m_n_2", "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>&iquest;Qu&eacute; rectas son paralelas al eje $x$ ?</p>", "minMarks": 0, "maxMarks": 0, "shuffleChoices": false, "displayType": "checkbox", "displayColumns": 0, "minAnswers": 0, "maxAnswers": 0, "warningType": "none", "showCellAnswerState": true, "choices": ["<p>$A_0$</p>", "<p>$B_0$</p>", "<p>$C_0$</p>", "<p>$D_0$</p>", "<p>$E_0$</p>", "Ninguna de estas"], "matrix": ["0", "0", 0, "2", "0", 0], "distractors": ["", "", "", "", "", ""]}, {"type": "m_n_2", "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>&iquest;Qu&eacute; rectas son paralelas a la recta con ecuaci&oacute;n: $y=\\simplify{{muniq}x+{c1}}$?</p>", "minMarks": 0, "maxMarks": 0, "shuffleChoices": false, 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