{"id":"cb_question_bank:06f7c0c4-b7b3-4e9d-8e26-2a0d52fc0749","source_id":"cb_question_bank","source_item_id":"06f7c0c4-b7b3-4e9d-8e26-2a0d52fc0749","external_id":null,"ibn":"029556-DC","question_id":"3cdbf026","program":"SAT","module":"math","domain_code":"H","domain":"Algebra","skill_code":"H.C.","skill":"Linear equations in two variables","difficulty":"H","score_band":6,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"The graph of the equation a, x plus k y, equals 6 is a line in the xy -plane, where a and k are constants. If the line contains the points with coordinates negative 2 comma negative 6 and 0 comma negative 3 , what is the value of k ?","stimulus":"","stimulus_html":null,"stem_html":"<p class=\"stem_paragraph \">The graph of the equation <span class=\"math_expression \"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/8ee0613f884b2bfdd8f1ac7ac59500e0e6e7fb12c7dcd5cad02c5bd1d5b06d1f\" alt=\"a, x plus k y, equals 6 \"></span></span> is a line in the <span class=\"italic \">xy</span>-plane, where <span class=\"italic\">a</span> and <span class=\"italic\">k </span>are constants. If the line contains the points <span class=\"math_expression \"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/ebc5cc036413fad1921c428eefe65f1377ff774201ef6837d3565657f529c8b3\" alt=\"with coordinates negative 2 comma negative 6 \"></span></span>and <span class=\"math_expression \"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/28d76d98272448b125e82cd28ab4c538d69f8e446d63762b8605360d6aefd2ca\" alt=\"0 comma negative 3\"></span></span>, what is the value of <span class=\"italic\">k </span>?</p>\n","rationale_html":"<p>Choice A is correct. The value of <span class=\"italic\">k</span> can be found using the slope-intercept form of a linear equation, <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. The equation <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/8ee0613f884b2bfdd8f1ac7ac59500e0e6e7fb12c7dcd5cad02c5bd1d5b06d1f\" alt=\"a, x plus, k y equals 6 \"></span> can be rewritten in the form <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/61c454ca341a0a50f9dde1aa1cfdd2243b0872d5cfdc15cfabf72e99292e8653\" alt=\"y equals, the negative of the fraction a, x, over k, end fraction, plus, the fraction 6 over k\"></span>. One of the given points, <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/28d76d98272448b125e82cd28ab4c538d69f8e446d63762b8605360d6aefd2ca\" alt=\"with coordinates 0 comma negative 3\"></span>, is the <span class=\"italic\">y</span>-intercept. Thus, the <span class=\"italic\">y</span>-coordinate of the <span class=\"italic\">y</span>-intercept <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/b62558094601a23d6fe95ffbc037ca0c41dd10264b6e51f4163b9ed575c135a3\" alt=\"negative 3\"></span> must be equal to <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/614eefba29ccd25f6968646f0fa62d8a2e574a50a02d7710fdd7b423ff4bd2cb\" alt=\"the fraction 6 over k\"></span>. Multiplying both sides by <span class=\"italic\">k</span> gives <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/55a2ec7b22543a886503a211da77aa88eccdc0221341df085a3e79d83b9b15c3\" alt=\"negative 3 k, equals 6\"></span>. Dividing both sides by <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/b62558094601a23d6fe95ffbc037ca0c41dd10264b6e51f4163b9ed575c135a3\" alt=\"negative 3\"></span> gives <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/d6f3effe988ed425d1b4f35167add0e34e5e8bc34f6982a94b1ccb1cbce3f9ce\" alt=\"k equals negative 2\"></span>.</p><p>Choices B, C, and D are incorrect and may result from errors made rewriting the given equation.</p><p></p>\n","correct_answer":["A"],"has_media":true,"has_mathml":false,"has_table":false,"source_created_at":"2023-08-02T20:25:59.626000+00:00","source_updated_at":"2023-08-02T20:25:59.626000+00:00","options":[{"label":"A","content_html":"<span class=\"choice_cell align:right \">\n            <span class=\"math_expression \">\n              <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/ce74cbabbaf45617e6561aad72315be422e849fe95e17b32d71443c7ee5c57e7\" alt=\"negative 2\"></span></span>\n          </span>\n","ord":0},{"label":"B","content_html":"<span class=\"choice_cell align:right \">\n            <span class=\"math_expression \">\n              <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/b3ef0bab498e581649a76baff7488f24fc7f565702b5178801873c0eccc8d6a5\" alt=\"negative 1\"></span></span>\n          </span>\n","ord":1},{"label":"C","content_html":"<span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/d870b3a6c89096490c39cc291dea5fd94193a953487d36d45d7f8548ac0b8f4e\" alt=\"2\"></span>\n","ord":2},{"label":"D","content_html":"<span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/b35ae18904fb781bd47e663cf02b992965491e4f50b31194e7d69870143879cd\" alt=\"3\"></span>\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}}