{"id":"cb_question_bank:a97e5c0c-12f5-4ab5-ba8a-f03e41afddb9","source_id":"cb_question_bank","source_item_id":"a97e5c0c-12f5-4ab5-ba8a-f03e41afddb9","external_id":null,"ibn":"029626-DC","question_id":"0366d965","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":"spr","answer_source":"rationale","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"The table above shows the coordinates of three points on a line in the xy -plane, where k and n are constants. If the slope of the line is 2, what is the value of k plus n ?","stimulus":"x y 3 7 k 11 12 n","stimulus_html":"<div class=\"stimulus_reference \">\n\t<div class=\"passage \">\n\t\t<div class=\"prose style:1 \">\n\t\t\t<div>\n\t\t\t\t<table class=\"tableWithBorder\" style=\"width:100px;\"><tbody><tr><td class=\"tableWithBorderTd td63922122-6f0a-42d5-8436-0568254f68a7\"><span class=\"italic \">x</span></td>\n\t\t\t\t\t\t\t<td class=\"tableWithBorderTd tdee6d7c90-61fd-4930-b110-fea327b8dc33\"><span class=\"italic \">y</span></td>\n\t\t\t\t\t\t</tr><tr><td class=\"tableWithBorderTd td74cacaff-5d54-4ac5-9340-c330ee1b3af6\">3</td>\n\t\t\t\t\t\t\t<td class=\"tableWithBorderTd tdab6afaf9-f239-4290-9260-53f4452c8bc6\">7</td>\n\t\t\t\t\t\t</tr><tr><td class=\"tableWithBorderTd tdb50c6923-32fc-468c-88f3-6ba3ebdf3d1b\"><span class=\"italic \">k</span></td>\n\t\t\t\t\t\t\t<td class=\"tableWithBorderTd td2c367f77-8b0c-4544-b3c2-edd8d2514d11\">11</td>\n\t\t\t\t\t\t</tr><tr><td class=\"tableWithBorderTd td00feb96a-dc80-4ba2-9c84-1c5c2ae6db4b\">12</td>\n\t\t\t\t\t\t\t<td class=\"tableWithBorderTd td7aff6f55-fbc1-4607-bb01-7f91a15db134\"><span class=\"italic \">n</span></td>\n\t\t\t\t\t\t</tr></tbody></table></div>\n\t\t</div>\n\t</div>\n</div>\n","stem_html":"<p class=\"stem_paragraph \">The table above shows the coordinates of three points on a line in the <span class=\"italic \">xy</span>-plane, where <span class=\"italic\">k</span> and <span class=\"italic\">n</span> are constants. If the slope of the line is 2, what is the value of <span class=\"math_expression \"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/fdb29fb12da94dce2e18dc6828ecec6b917f17d34ba6c77ef0ca9ddc4a50f865\" alt=\"k plus n\"></span>&nbsp;</span>?</p>\n","rationale_html":"<p>The correct answer is 30. The slope of a line can be found by using the slope formula, <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/a03975b16d4ea2c3b86d4b581b9e016521425404cedaa5512efb6e3d64a3280f\" alt=\"the fraction with numerator y sub 2 minus y sub 1, and denominator x sub 2 minus x sub 1, end fraction\"></span>. It’s given that the slope of the line is 2; therefore, <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/fe5d471d63b5e901ba97aa6f810024e628a3d4f375615889147d80d30421e83f\" alt=\"the fraction with numerator y sub 2 minus y sub 1, and denominator x sub 2 minus x sub 1, end fraction, equals 2\"></span>. According to the table, the points <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/09e22ddc129a62bf94c0084a1763d74a7083afd746f1c17d566a051c50f9d4d3\" alt=\"with coordinates 3 comma 7\"></span> and <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/55776899f3958bc6395b40d2896e6e7744b30f979b90673a2a548990d6192932\" alt=\"with coordinates k comma 11\"></span> lie on the line. Substituting the coordinates of these points into the equation gives <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/a4a0edcfe99cbe3d1062a5d791113936d76d42b895a1ff89ba53e5ad7e8a19e4\" alt=\"the fraction with numerator 11 minus 7, and denominator k minus 3, end fraction, equals 2\"></span>. Multiplying both sides of this equation by <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/ab406836dc2e6bdc86ae5f121afd457197468dfe53b2774d54e0d2b53937c35b\" alt=\"k minus 3 \"></span> gives <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/dea53e34716ca3e59421715e9ed97d7742e351f61794a304248c6d715c5845db\" alt=\"11 minus 7, equals, 2 times, open parenthesis, k minus 3, close parenthesis\"></span>, or <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/baaccb506c0425085339b4be40cd7ba975a32a8b2264495c39b5d6851007c4c2\" alt=\"11 minus 7, equals, 2 k minus 6\"></span>. Solving for <span class=\"italic\">k</span> gives <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/f9ad746316c95d97c528c729003117b0de250d840e78abf6dcdd9eb315dcdad1\" alt=\"k equals 5\"></span>. According to the table, the points <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/09e22ddc129a62bf94c0084a1763d74a7083afd746f1c17d566a051c50f9d4d3\" alt=\"with coordinates 3 comma 7\"></span> and <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/1f07c409e6262013fc87ba6dfe16b532e666bb97839fda08dd3fa15634adc5dd\" alt=\"with coordinates 12 comma n\"></span> also lie on the line. Substituting the coordinates of these points into <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/fe5d471d63b5e901ba97aa6f810024e628a3d4f375615889147d80d30421e83f\" alt=\"the fraction with numerator y sub 2 minus y sub 1, and denominator x sub 2 minus x sub 1, end fraction, equals 2 \"></span> gives <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/423a94b4bd83fc6fe26978390b7298d79c4488d92add05e417229b9eab22e9f1\" alt=\"the fraction with numerator n minus 7, and denominator 12 minus 3, end fraction, equals 2\"></span>. Solving for <span class=\"italic\">n</span> gives <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/84bbd73c0afc87e22cbe2e2e9169a6652af84fb2a02218c7459ee5af35b3023f\" alt=\"n equals 25\"></span>. Therefore, <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/dc5771eb3c8670f7290c1d9e749923f1e9b6972aa12f13af42272e999cb3345e\" alt=\"k plus n, equals, 5 plus 25\"></span>, or 30.</p>\n","correct_answer":["30"],"has_media":true,"has_mathml":false,"has_table":true,"source_created_at":"2023-08-02T20:25:59.626000+00:00","source_updated_at":"2023-08-02T20:25:59.626000+00:00","options":[],"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}}