","topicId":"04c3a7e9-b65d-4534-994c-eaf468f48bb5","topicSlug":"straight-line-models","cards":[{"id":"d5d337fb-7a04-4856-aaca-97dabcf3cd70","cardType":"cloze","front":"A non-vertical straight line model has the form $\\text{[...]}$.","back":"A non-vertical straight line model has the form $\\boxed{y=mx+c}$.","points":null,"mcqOptions":null},{"id":"46b7274c-1f19-45ce-80b9-0347c73ed493","cardType":"basic","front":"What does $m>0$ predict about $y$ as $x$ increases?","back":"$$y$ increases.","points":1,"mcqOptions":null},{"id":"eb77d5b2-dfda-4885-87b5-47dd3a4da4f8","cardType":"basic","front":"What does $m<0$ predict about $y$ as $x$ increases?","back":"$$y$ decreases.","points":1,"mcqOptions":null},{"id":"1b5633de-cb46-49e4-a86c-c52ff40dfc93","cardType":"basic","front":"What does $m=0$ predict about $y$ as $x$ increases?","back":"$$y$ remains constant.","points":1,"mcqOptions":null},{"id":"53e50b7e-8242-47c3-bb62-a4928d1ee081","cardType":"cloze","front":"The units of a gradient are $\\text{[...]}$.","back":"The units of a gradient are $\\boxed{rac{\\text{units of }y}{\\text{units of }x}}$.","points":null,"mcqOptions":null},{"id":"473e4c8a-ccab-4460-87dc-bccdffe0fb0e","cardType":"basic","front":"In $C=0.45d+8$, what does the gradient represent?","back":"The cost increases by £0.45 per kilometre.","points":1,"mcqOptions":null},{"id":"e7014244-001f-4c6f-a0d3-5d1f1d7f964a","cardType":"basic","front":"In $C=0.45d+8$, what does the intercept represent?","back":"A fixed charge of £8.","points":1,"mcqOptions":null},{"id":"0394f63b-fc93-4b95-b4bf-68a191195fe8","cardType":"basic","front":"What must be checked before interpreting an intercept in context?","back":"Whether $x=0$ is possible and within the model's range.","points":2,"mcqOptions":null},{"id":"207cbeeb-8f03-4347-8be9-63a08020ac3f","cardType":"cloze","front":"A straight line model assumes equal increases in $x$ produce [ ].","back":"A straight line model assumes equal increases in $x$ produce equal changes in $y$.","points":null,"mcqOptions":null},{"id":"02c6107c-a3ab-4521-b1ff-c68dcecb0c10","cardType":"cloze","front":"For points $(x_1,y_1)$ and $(x_2,y_2)$, the gradient is $\\text{[...]}$.","back":"For points $(x_1,y_1)$ and $(x_2,y_2)$, the gradient is $\\boxed{m=\\frac{y_2-y_1}{x_2-x_1}}$.","points":null,"mcqOptions":null},{"id":"52ef2311-e5b2-46fa-97e2-3c243d9948d1","cardType":"basic","front":"After finding $m$ from two points, how is $c$ found?","back":"Substitute either point into $y=mx+c$.","points":1,"mcqOptions":null},{"id":"365b2b3d-d5b0-4355-afaa-08f1f2f82d1e","cardType":"basic","front":"What straight line model fits $(2,18500)$ and $(6,13700)$?","back":"$V=20900-1200t$.","points":2,"mcqOptions":null},{"id":"4e586303-64b8-4d31-aa3e-3e29cabbb484","cardType":"basic","front":"In $V=20900-1200t$, interpret the gradient in context.","back":"The machine's value decreases by £1,200 per year.","points":1,"mcqOptions":null},{"id":"6157dce6-1ff1-429d-a095-049c32f6d6cd","cardType":"basic","front":"A liquid cools by $2.5$ °C per minute and is $68$ °C after $4$ minutes. What is its model?","back":"$T=78-2.5t$.","points":2,"mcqOptions":null},{"id":"71beed3a-d974-488f-ae37-718dba70d1d7","cardType":"basic","front":"Using $V=20900-1200t$, what value is predicted after $8$ years?","back":"The model predicts £11,300.","points":1,"mcqOptions":null},{"id":"fac2fa25-3e5f-4119-a807-9be52f7ca700","cardType":"basic","front":"Using $V=20900-1200t$, when is the value predicted to reach £5,000?","back":"After $13.25$ years.","points":2,"mcqOptions":null},{"id":"10a1a923-180e-4467-bb7f-529f3574ef0e","cardType":"basic","front":"How is the input

1.3.3 Straight line models Flashcards

1.3.3 Straight line models Flashcards