{"id":"cb_question_bank:d8d8bb8c-c0e9-4180-8176-b504608e86a5","source_id":"cb_question_bank","source_item_id":"d8d8bb8c-c0e9-4180-8176-b504608e86a5","external_id":null,"ibn":"045840-DC","question_id":"a7a14e87","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":"In the xy -plane, line k is defined by x plus y equals 0 . Line j is perpendicular to line k , and the y -intercept of line j is the point with coordinates 0 comma 3 . Which of the following is an equation of line j ?","stimulus":"","stimulus_html":null,"stem_html":"<p class=\"stem_paragraph \">In the <span class=\"italic \">xy</span>-plane, line <span class=\"italic\">k</span> is defined by <span class=\"math_expression \"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/334cbd768f07528a2205ad0175f4b12990fdc2dd693d1ee192303540a5f0f491\" alt=\"x plus y equals 0\"></span></span>. Line <span class=\"italic\">j</span> is perpendicular to line <span class=\"italic\">k</span>, and the <span class=\"italic \">y</span>-intercept of <span class=\"formatted_line_break delivery_mode:Both \"></span>line <span class=\"italic\">j</span> is <span class=\"math_expression \"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/18ef80b67575a6bd348af21c284b6114c5668aad7ed5c2b152bdc5ba431a094d\" alt=\"the point with coordinates 0 comma 3\"></span></span>. Which of the following is an equation of line <span class=\"italic \">j</span> ?</p>\n","rationale_html":"<p>Choice D is correct. It’s given that line <span class=\"italic\">j</span> is perpendicular to line<span class=\"italic\"> k </span>and that line <span class=\"italic\">k</span> is defined by the equation <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/334cbd768f07528a2205ad0175f4b12990fdc2dd693d1ee192303540a5f0f491\" alt=\"x plus y, equals 0\"></span>. This equation can be rewritten 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> represents the slope of the line and <span class=\"italic\">b</span> represents the <span class=\"italic\">y</span>-coordinate of the <span class=\"italic\">y</span>-intercept of the line, by subtracting <span class=\"italic\">x</span> from both sides of the equation, which yields <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/91f69d96b1340cc83f1f88d77e05acc4daa7dc9b1114c39a89dea03795c6e46c\" alt=\"y equals, negative x\"></span>. Thus, the slope of line <span class=\"italic\">k</span> is <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/c1e573ec087416273e06563cee97890abeeed317436562b06a92c8920d4c759d\" alt=\"negative 1\"></span>. Since line <span class=\"italic\">j</span> and line <span class=\"italic\">k</span> are perpendicular, their slopes are opposite reciprocals of each other. Thus, the slope of line <span class=\"italic\">j</span> is 1. It’s given that the <span class=\"italic\">y</span>-intercept of line <span class=\"italic\">j</span> is <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/3dc5232d4a3e4139a60e7c3ac0d4665650de3ba8a775385eb9e3311e59c72324\" alt=\"the point with coordinates 0 comma 3\"></span>. Therefore, the equation for line <span class=\"italic\">j</span> in slope-intercept form is <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/43a63d77038494f0ee3dbec46c868a194336f1e786522d14d7acc417b252cb86\" alt=\"y equals, x plus 3\"></span>, which can be rewritten as <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/dda84d8caf082ee82f68af24d2e029554f2285ec25bb2a3fdc2f61b9587d1d02\" alt=\"x minus y, equals negative 3\"></span>.</p><p>Choices A, B, and C are incorrect and may result from conceptual or calculation errors.</p><p></p>\n","correct_answer":["D"],"has_media":true,"has_mathml":false,"has_table":false,"source_created_at":"2023-08-02T20:25:59.628000+00:00","source_updated_at":"2023-08-02T20:25:59.628000+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/1f3decd5a09725c340150516af87ad54fdc48a076b00ba7c4a44a17fe5d5abb0\" alt=\"x plus y, equals 3\"></span></span>\n          </p>\n","ord":0},{"label":"B","content_html":"<p class=\"choice_paragraph \">\n            <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/10610c9680892872190405c4aee4162518121bf03516462341a8125f2733e700\" alt=\"x plus y, equals negative 3\"></span></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/6ad5b75e0b56e315baba5e1cbe3835812ff33c50c5410186d11a9d88643b3b66\" alt=\"x minus y, equals 3\"></span></span>\n          </p>\n","ord":2},{"label":"D","content_html":"<p class=\"choice_paragraph \">\n            <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/dda84d8caf082ee82f68af24d2e029554f2285ec25bb2a3fdc2f61b9587d1d02\" alt=\"x minus y, equals negative 3\"></span></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}}