{"id":"cb_question_bank:7abb0437-c5ee-4ea3-83d7-9f2e5089ece5","source_id":"cb_question_bank","source_item_id":"7abb0437-c5ee-4ea3-83d7-9f2e5089ece5","external_id":null,"ibn":"025468-DC","question_id":"c22b5f25","program":"SAT","module":"math","domain_code":"H","domain":"Algebra","skill_code":"H.B.","skill":"Linear functions","difficulty":"M","score_band":5,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"In the xy -plane, the points with coordinates negative 2 comma 3 and 4 comma negative 5 lie on the graph of which of the following linear functions?","stimulus":"","stimulus_html":null,"stem_html":"<p class=\"stem_paragraph \">In the <span class=\"italic \">xy</span>-plane, the points <span class=\"math_expression \"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/078935707b2cbcfda587933a2af89f5fcdd712d683fc6d866b7e486ba1b07532\" alt=\"with coordinates negative 2 comma 3 \"></span></span> and <span class=\"math_expression \"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/5ec70c205e57d47e311915b4733073f723ef467080a0acfa5c08374d121a5d64\" alt=\"4 comma negative 5 \"></span></span> lie on the graph of which of the following linear functions?</p>\n","rationale_html":"<p>Choice C is correct. A linear function can be written in the form <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/85d346e80696592103a24156028b524124e60208306aaa1d2b81366c09e2f8e4\" alt=\"f of x  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 of the line. The slope of the graph can be found using the formula <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/d90665e9527746054088c372f023f7eaa687ac5da59918408884c2d405e79dcc\" alt=\"m equals, the fraction with numerator y sub 2 minus y sub 1, and denominator x sub 2 minus x sub 1, end fraction\"></span>. Substituting the values of the given points into this formula yields <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/b8c4a1dbf975f008f1c29acb9888dec6e3b03f93ab900d0e284b303af1223007\" alt=\"m equals, the fraction with numerator negative 5 minus 3, and denominator 4 minus negative 2, end fraction \"></span> or <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/e315220e50b8596d630160646dab2f8396ace124f84c864b38e796b90a286e4d\" alt=\"m equals, negative 8 over 6\"></span>, which simplifies to <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/3b9feba0990271b818033123b3d18497ea8ed44baa7dae89f6e57e2284842217\" alt=\"m equals, negative four thirds\"></span>. Only choice C shows an equation with this slope.<br><br>\nChoices A, B, and D are incorrect and may result from computation errors or misinterpreting the given information.</p>\n","correct_answer":["C"],"has_media":true,"has_mathml":false,"has_table":false,"source_created_at":"2023-08-02T20:25:59.618000+00:00","source_updated_at":"2023-08-02T20:25:59.618000+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/9d7210aeff368516b749616a29e7abb5a3fcd431e53215b44a7dcc9521cc15b1\" alt=\"f of x equals, x plus 5\"></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/4cb15c0f603e6918ee555862472b409db22fe1c1316d46a8601be4b6eb22854d\" alt=\"f of x equals, one half x, plus 4\"></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/7373b885b5d19d8f550003e44d5e3a5ea9937267cd619a06574cc26062e7a600\" alt=\"f of x equals, negative, four thirds x, plus one third\"></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/6b75d704d3751d712d06af4ab190e3d8be0f8cf639890fab76144b1bf4b5057e\" alt=\"f of x equals, negative, three halves x, plus 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}}