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Compare the gradients of 3 lines and choose the steepest. Part of HELM Book 2.5.1.

", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "

Which of the following lines has the steepest gradient?

", "advice": "

When the line is written in the form $y=ax+b$, the constant $a$ is the gradient. Work out the gradient for each line and then determine which has the greatest magnitude (absolute value).

", "rulesets": {}, "extensions": ["jsxgraph"], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"diagram1": {"name": "diagram1", "group": "Ungrouped variables", "definition": "jessiecode(\n 250,250,[-0.5,29, 6,-2],\n \"\"\"\n A= point(0,3) <> >>;\n B=point(5,23) <> >>;\n \n side_a = line(A,B);\n \n x=text(5.7,-1,\"x\"); // no idea how to get axis labels otherwise...\n y=text(-0.3,28,\"y\");\n \n \"\"\",\n [\n \"axis\": true\n ]\n)", "description": "", "templateType": "anything", "can_override": false}, "diagram2": {"name": "diagram2", "group": "Ungrouped variables", "definition": "jessiecode(\n 250,250,[-3,15, 3,-10],\n \"\"\"\n A= point(0,-3) <>,color:\"black\" >>;\n B=point(2,5) <>,color:\"black\" >>;\n line1 = line(A,B) <>;\n \n C= point(0,0) <>,color:\"blue\" >>;\n D=point(2,8) <>,color:\"blue\" >>;\n line1 = line(C,D) <>;\n \n E= point(0,5) <>,color:\"red\" >>;\n F=point(2,13) <>,color:\"red\" >>;\n line1 = line(E,F) <>;\n \n x=text(2.7,-2,\"x\"); // no idea how to get axis labels otherwise...\n y=text(-0.4,14,\"y\");\n \n \"\"\",\n [\n \"axis\": true\n ]\n)", "description": "", "templateType": "anything", "can_override": false}, "c": {"name": "c", "group": "Ungrouped variables", "definition": "[random(1..9),\n random(1..9),\n 1/random(2..9),\n 1/random(2..9),\n random(1..9),\n random(1..9),\n random(-9..9 except 0)\n ]", "description": "

constants for task 2

", "templateType": "anything", "can_override": false}, "diagram3": {"name": "diagram3", "group": "Ungrouped variables", "definition": "jessiecode(\n 250,250,[-3,15, 3,-10],\n \"\"\"\n A= point(0,3) <>,color:\"black\" >>;\n B=point(1,6) <>,color:\"black\" >>;\n line1 = line(A,B) <>;\n \n C= point(0,3) <>,color:\"blue\" >>;\n D=point(1,8) <>,color:\"blue\" >>;\n line1 = line(C,D) <>;\n \n E= point(0,3) <>,color:\"red\" >>;\n F=point(1,1) <>,color:\"red\" >>;\n line1 = line(E,F) <>;\n \n x=text(2.7,-2,\"x\"); // no idea how to get axis labels otherwise...\n y=text(-0.4,14,\"y\");\n \n \"\"\",\n [\n \"axis\": true\n ]\n)", "description": "

Diagram for Example 12

", "templateType": "anything", "can_override": false}, "d": {"name": "d", "group": "Ungrouped variables", "definition": "[\n random(2..9),\n random(1..9),\n 1/random(2..9),\n random(1..9),\n random(1..9),\n random(2..9),\n random(1..9)\n ]", "description": "

constants for task 3

", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["diagram1", "diagram2", "c", "diagram3", "d"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"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": "radiogroup", "displayColumns": 0, "showCellAnswerState": true, "choices": ["$\\displaystyle{y=\\frac{17x+4}{5} }$", "$\\displaystyle{y=9x-2 }$", "$\\displaystyle{y=\\frac{1}{3}x+4 }$"], "matrix": [0, "1", 0], "distractors": ["This line has gradient 17/5 which is not the steepest.", "This line has gradient 9, which is the steepest.", "This line has gradient 1/3, which is not the steepest."]}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "contributors": [{"name": "Merryn Horrocks", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4052/"}]}]}], "contributors": [{"name": "Merryn Horrocks", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4052/"}]}