{"id":"cb_question_bank:95aaed02-aeca-46ca-bd74-d49e88fa5cef","source_id":"cb_question_bank","source_item_id":"95aaed02-aeca-46ca-bd74-d49e88fa5cef","external_id":null,"ibn":"027702-DC","question_id":"9296553d","program":"SAT","module":"math","domain_code":"Q","domain":"Problem-Solving and Data Analysis","skill_code":"Q.D.","skill":"Two-variable data: Models and scatterplots","difficulty":"E","score_band":2,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"Which of the following could be an equation for a line of best fit for the data in the scatterplot?","stimulus":"The figure presents a scatterplot in the x y plane. The numbers 0 through 5, in increments of 1, are indicated along the x-axis. The numbers 0 through 6, in increments of 1, are indicated along the y-axis. There are 11 data points in the scatterplot. The data points begin on the y-axis at 6, and trend almost linearly downward and to the right. The data points end at the point with coordinates 5 comma 1.","stimulus_html":"<div class=\"stimulus_reference \">\n        <div class=\"standalone_image \">\n          <img src=\"/api/assets/772c705cd3e8487aaf726cb4a4a6b08ef6601674ac64f62ae532121735566cc8\" alt=\"The figure presents a scatterplot in the x y plane. The numbers 0 through 5, in increments of 1, are indicated along the x-axis. The numbers 0 through 6, in increments of 1, are indicated along the y-axis. There are 11 data points in the scatterplot. The data points begin on the y-axis at 6, and trend almost linearly downward and to the right. The data points end at the point with coordinates 5 comma 1.\" width=\"104\" height=\"131\"></div>\n      </div>\n","stem_html":"<p class=\"stem_paragraph \">Which of the following could be an equation for a line of best fit for the data in the scatterplot?</p>\n","rationale_html":"<p>Choice A is correct. A line of best fit for the data in a scatterplot is a line that follows the trend of the data with approximately half the data points above and half the data points below the line. Based on the given data, a line of best fit will have a positive <span class=\"italic\">y</span>-intercept on or near the point <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/0987d991ac5e8b483893e56be19ebc31eb74df06e7894a23180ebb031241934d\" alt=\"with coordinates 0 comma 6\"></span> and a negative slope. All of the choices are in slope-intercept form <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/39dda01984e771026b6a8a741d3ebb66f1a29f1e81583b67f8d50f6e2dbb783e\" alt=\"y equals, m x plus b\"></span>, where <span class=\"italic\">m</span> is the slope and <span class=\"italic\">b</span> is the <span class=\"italic\">y</span>-coordinate of the <span class=\"italic\">y</span>-intercept. Only choice A is an equation of a line with a positive <span class=\"italic\">y</span>-intercept at <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/0987d991ac5e8b483893e56be19ebc31eb74df06e7894a23180ebb031241934d\" alt=\"the point with coordinates 0 comma 6 \"></span> and a negative slope, <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/c1e573ec087416273e06563cee97890abeeed317436562b06a92c8920d4c759d\" alt=\"negative 1\"></span>.</p><p>Choice B is incorrect. This equation is for a line that has a negative <span class=\"italic\">y</span>-intercept, not a positive <span class=\"italic\">y</span>-intercept. Choices C and D are incorrect and may result from one or more sign errors and from switching the values of the <span class=\"italic\">y</span>-intercept and the slope in the equation.</p><p></p>\n","correct_answer":["A"],"has_media":true,"has_mathml":false,"has_table":false,"source_created_at":"2023-08-02T20:25:59.621000+00:00","source_updated_at":"2023-08-02T20:25:59.621000+00:00","options":[{"label":"A","content_html":"<p class=\"choice_paragraph \">\n            <span class=\"math_expression \">\n              <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/e0a361515dd5f8d357137bb2b9269ce4014001d364d9663b4c1fd6a33c0fa302\" alt=\"y equals, negative x, plus 6\"></span></span>\n          </p>\n","ord":0},{"label":"B","content_html":"<p class=\"choice_paragraph \">\n            <span class=\"math_expression \">\n              <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/8871a4f88e48cc68d954effae7911342eae8bafefa7c236e65c1b026d5e60f33\" alt=\"y equals, negative x, minus 6\"></span></span>\n          </p>\n","ord":1},{"label":"C","content_html":"<p class=\"choice_paragraph \">\n            <span class=\"math_expression \">\n              <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/a1f1721159be1cc9220581becd52b45445487f3c5e9d5020f7bb4890f415f126\" alt=\"y equals, 6 x, plus 1\"></span></span>\n          </p>\n","ord":2},{"label":"D","content_html":"<p class=\"choice_paragraph \">\n            <span class=\"math_expression \">\n              <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/b04970d850b0c5951398adf48c0fd68b63d7b4aaadf71782242c365e7a2f39ce\" alt=\"y equals, 6 x, minus 1\"></span></span>\n          </p>\n","ord":3}],"attribution":{"source_id":"cb_question_bank","source_name":"College Board digital SAT question bank (community dump)","rights_holder":"College Board","canonical_url":"https://satsuitequestionbank.collegeboard.org/","retrieved_from":"https://raw.githubusercontent.com/mdn522/sat-question-bank/main/data/cb-digital-questions.json","attribution":"SAT practice questions © College Board, from the official SAT Suite Question Bank. Retrieved via the community dump at github.com/mdn522/sat-question-bank.","disclaimer":"SAT® and PSAT/NMSQT® are trademarks registered by the College Board, which is not affiliated with, does not sponsor, and does not endorse this project.","license":"College Board copyright; source repository carries no licence. Local use only.","redistributable":false,"item_count":2017}}