// Numbas version: finer_feedback_settings
{"name": "Linear graphs: Find equation of a line 1", "extensions": ["geogebra"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Linear graphs: Find equation of a line 1", "tags": [], "metadata": {"description": "<p>Find the equation from the image of graph</p>", "licence": "None specified"}, "statement": "<p><em>You can zoom and pan this image</em></p>\n<p>{app}<br/><br/><br/></p>", "advice": "<p><strong>To find the gradient</strong></p>\n<p>Firstly draw a right angled 'step' from left to right. This triangle can be anywhere, but it is more helpful for it to have corners on the vertices (whole number points) of the graph and it is easier to calculate with postive numbers.</p>\n<p>{app_advice}</p>\n<p>Before we start to calculate, notice that the line is {uod}, so the gradient will be {pon} and the line is {sos}, so the absolute value of the number will be {mol}.<br/><br/>Now find the coordinates of the places your triangle meets the line</p>\n<p>$(x_1,y_1)=(\\var{ax},\\var{ay})$ and $(x_2,y_2)=(\\var{bx},\\var{by})$</p>\n<p>We need to compare the 'rise on the y-axis' to the 'run across the x-axis', we can say that:</p>\n<p>$\\text{gradient} = \\frac{\\text{rise}}{\\text{run}}$</p>\n<p>This is equivalent to using the formula:<br/><br/>$&nbsp; m = \\frac{y_2 - y_1}{x_2 - x_1} $</p>\n<p>and substitute the coordinates of the vertices of the triangle:<br/><br/>$\\begin{split} &amp;\\, m = \\frac{\\var{by} - \\var{ay}}{\\var{bx} - \\var{ax}} \\\\ &nbsp;<br/>&amp;\\, = \\frac{\\var{by-ay}}{\\var{bx-ax}} \\\\&nbsp;<br/>&amp;\\, &nbsp;= \\var[fractionNumbers]{m} \\\\<br/>\\end{split} $</p>\n<p><strong></strong></p>\n<p><strong>To complete the equation</strong></p>\n<p>You can either read the intercept from the graph (if it is obvious where the line cuts the y-axis) or you can calculate it.</p>\n<p>We know there gradient so we can write $y=\\var{m}x+c$ and rearrange to give us:</p>\n<p>$c = \\simplify[all]{y - {m}x}$<br/><br/>Then subsitute the value of $x$ and $y$ from any point on the line, let's use $(\\var{ax},\\var{ay})$ to give</p>\n<p>$c = \\var{ay} \\simplify[all]{- {m}} \\times \\var{ax}$</p>\n<p>$c = \\var{c}$</p>\n<p>So the final equation is&nbsp;</p>\n<p>$y = \\simplify[collectNumbers, zeroterm,unitfactor]{{m}x +{c}}$</p>", "rulesets": {}, "extensions": ["geogebra"], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"app": {"name": "app", "group": "Ungrouped variables", "definition": 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"uod": {"name": "uod", "group": "Ungrouped variables", "definition": "if(m=0,'horizontal',if(m=abs(m),'going up','going down'))", "description": "<p>if(m=abs(m),'positive','negative')</p>", "templateType": "anything", "can_override": false}, "ax": {"name": "ax", "group": "Ungrouped variables", "definition": "random(0,1)", "description": "", "templateType": "anything", "can_override": false}, "ay": {"name": "ay", "group": "Ungrouped variables", "definition": "random(0,1,2,3)", "description": "", "templateType": "anything", "can_override": false}, "bx": {"name": "bx", "group": "Ungrouped variables", "definition": "random(ax+1..3) \n", "description": "", "templateType": "anything", "can_override": false}, "by": {"name": "by", "group": "Ungrouped variables", "definition": "random(0..4 except ay)\n", "description": "", "templateType": "anything", "can_override": false}, "app_advice": {"name": "app_advice", "group": "Ungrouped variables", "definition": "geogebra_applet(\n  800,500,\n  [\n    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"variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Find the equation of the line.</p>", "answer": "y = {m}x + {c}", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": [{"name": "x", "value": ""}, {"name": "y", "value": ""}]}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "question", "contributors": [{"name": "Ruth Hand", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3228/"}]}]}], "contributors": [{"name": "Ruth Hand", "profile_url": 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