{"id":"cb_question_bank:e1d70cc8-1439-4e21-9e1a-c8910e0e089b","source_id":"cb_question_bank","source_item_id":"e1d70cc8-1439-4e21-9e1a-c8910e0e089b","external_id":null,"ibn":"029386-DC","question_id":"2eef7e61","program":"SAT","module":"math","domain_code":"H","domain":"Algebra","skill_code":"H.B.","skill":"Linear functions","difficulty":"E","score_band":1,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"The graph of the function f is a line in the xy -plane. If the line has slope three-fourths and f of 0, equals 3 , which of the following defines f ?","stimulus":"","stimulus_html":null,"stem_html":"<p class=\"stem_paragraph \">The graph of the function <span class=\"italic\">f</span> is a line in the <span class=\"italic \">xy</span>-plane. If the line has slope <span class=\"math_expression \"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/b66901330890b6e3cf57fc87badb8d20fda5cee27ab863f2ec195b83e585ed89\" alt=\"three-fourths \"></span></span> and <span class=\"math_expression \"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/28257e5c52672c2fdc2729da16b6dbe2c4a518219aed878a95441c406c05268c\" alt=\"f of 0, equals 3\"></span></span>, which of the following defines <span class=\"italic\">f</span>?</p>\n","rationale_html":"<p>Choice B is correct. The equation for the function <span class=\"italic\">f</span> in the <span class=\"italic\">xy</span>-plane can be represented by <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. Since it’s given that the line has a slope of <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/b66901330890b6e3cf57fc87badb8d20fda5cee27ab863f2ec195b83e585ed89\" alt=\"three fourths\"></span>, it follows that <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/e5ec975c5cb71ebb7b2a0fb4437eebdbceb0923f158346b80f4c0504587a30be\" alt=\"m equals three fourths \"></span> in <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>, which<span class=\"italic\"></span> yields <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/f1719c7747c5b0a6669db07daf10ec2a93e8261e7c2172ce16dd7c711aad9019\" alt=\"y equals, three fourths x, plus b\"></span>. It’s given that <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/28257e5c52672c2fdc2729da16b6dbe2c4a518219aed878a95441c406c05268c\" alt=\"f of 0 equals 3\"></span>. This implies that the graph of the function <span class=\"italic\">f</span> in the <span class=\"italic\">xy</span>-plane passes through the point <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/18ef80b67575a6bd348af21c284b6114c5668aad7ed5c2b152bdc5ba431a094d\" alt=\"with coordinates 0 comma 3\"></span>. Thus, the <span class=\"italic\">y</span>-coordinate of the <span class=\"italic\">y</span>-intercept of the graph is 3, so <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/815f2555f3430bc04271b955789f6b6d783109aab1757dfb0c9eaa8c9c258038\" alt=\"b equals 3\"></span> in <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/b3cc7d259bfb860d41c221928c89ecd7914437db6845013e5b2d259f18b183a1\" alt=\"f of x equals, three fourths x, plus b\"></span>, which <span class=\"italic\"></span>yields <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/59ad1ef4a67b2e01f0cc3d2b7f2ce5872be493311337e2687048598f982c22a3\" alt=\"f of x equals, three fourths x, plus 3\"></span>. Therefore, the equation <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/59ad1ef4a67b2e01f0cc3d2b7f2ce5872be493311337e2687048598f982c22a3\" alt=\"f of x equals, three fourths x, plus 3\"></span> defines the function <span class=\"italic\">f. </span></p><p>Choice A is incorrect and may result from a sign error for the <span class=\"italic\">y</span>-intercept. Choice C is incorrect and may result from using the denominator of the given slope as <span class=\"italic\">m</span> in <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>, in addition to a sign error for the <span class=\"italic\">y</span>-intercept. Choice D is incorrect and may result from using the denominator of the given slope as <span class=\"italic\">m</span> in <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>.</p><p></p>\n","correct_answer":["B"],"has_media":true,"has_mathml":false,"has_table":false,"source_created_at":"2023-08-02T20:25:59.625000+00:00","source_updated_at":"2023-08-02T20:25:59.625000+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/97465a4b92962c306a1705790e1a7580104267f53b84bf83f4aeaa12e4516d9d\" alt=\"f of x equals, three fourths x, minus 3\"></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/59ad1ef4a67b2e01f0cc3d2b7f2ce5872be493311337e2687048598f982c22a3\" alt=\"f of x equals, three fourths x, plus 3\"></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/4cf1066e2b58d62ac934cf5f3e0e56cb71f77c356c0866425f1eb9161526a487\" alt=\"f of x equals, 4 x, minus 3\"></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/161582a00b49dd2ce615cfae22fb312646fe37c37e3cfe78e69e13a02082b1f7\" alt=\"f of x equals, 4 x, plus 3\"></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}}