{"id":"cb_question_bank:93899c3a-2282-4a6e-aa42-0fc08824645e","source_id":"cb_question_bank","source_item_id":"93899c3a-2282-4a6e-aa42-0fc08824645e","external_id":null,"ibn":"10934-DC","question_id":"98d3393a","program":"SAT","module":"math","domain_code":"H","domain":"Algebra","skill_code":"H.C.","skill":"Linear equations in two variables","difficulty":"H","score_band":7,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"Line l in the xy -plane is perpendicular to the line with equation x equals 2 . What is the slope of line l ?","stimulus":"","stimulus_html":null,"stem_html":"<p class=\"stem_paragraph \">Line <span class=\"math_expression \"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/b3ed61300b239762a0f7bec1dc9a48ecd5e011d08d5338f426429aa3c459a067\" alt=\"l\"></span></span> in the <span class=\"italic\"><span class=\"formatted_text font_style:italic \">xy</span></span>-plane is perpendicular to the line with equation <span class=\"math_expression \"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/401169281090f4f1d9aafeeb928524e672d737cdce814b4e9256c5e06a42d325\" alt=\"x equals 2\"></span></span>. What is the slope of line <span class=\"math_expression \"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/b3ed61300b239762a0f7bec1dc9a48ecd5e011d08d5338f426429aa3c459a067\" alt=\"l\"></span></span>?</p>\n","rationale_html":"<p>Choice A is correct. It is given that line <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/b3ed61300b239762a0f7bec1dc9a48ecd5e011d08d5338f426429aa3c459a067\" alt=\"l\"></span> is perpendicular to a line whose equation is <span class=\"italic\">x</span> = 2. A line whose equation is a constant value of <span class=\"italic\">x</span> is vertical, so <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/b3ed61300b239762a0f7bec1dc9a48ecd5e011d08d5338f426429aa3c459a067\" alt=\"l\"></span> must therefore be horizontal. Horizontal lines have a slope of 0, so <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/b3ed61300b239762a0f7bec1dc9a48ecd5e011d08d5338f426429aa3c459a067\" alt=\"l\"></span> has a slope of 0.</p><p>Choice B is incorrect. A line with slope&nbsp;<span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/c32675bf7ded3a05413c4197ed13d278dd4cd18b26f7e63428e41d3fb6ed70bb\" alt=\"negative one half\"></span> is perpendicular to a line with slope 2. However, the line with equation <span class=\"italic\">x</span> = 2 is vertical and has undefined slope (not slope of 2).&nbsp;Choice C is incorrect. A line with slope –2 is perpendicular to a line with slope <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/acd304db4db3ee4a427462753769f86b9941b320104a3856da731c39db5d894c\" alt=\"one half\"></span>. However, the line with equation<span class=\"italic\"> x</span> = 2 has undefined slope (not slope of <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/acd304db4db3ee4a427462753769f86b9941b320104a3856da731c39db5d894c\" alt=\"one half\"></span>). Choice D is incorrect; this is the slope of the line <span class=\"italic\">x</span> = 2 itself, not the slope of a line perpendicular to it.</p><p></p>\n","correct_answer":["A"],"has_media":true,"has_mathml":false,"has_table":false,"source_created_at":"2023-08-02T20:25:59.638000+00:00","source_updated_at":"2023-08-02T20:25:59.638000+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/e646b570dc3598aa1fe55743f6c749ef456a13deb8575aca77a309272b8cbc26\" alt=\"0\"></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/c32675bf7ded3a05413c4197ed13d278dd4cd18b26f7e63428e41d3fb6ed70bb\" alt=\"negative one half\"></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/a546b5be2c97283e2d1e93605f422844d5a87f3418a61a7d23019eb596b64f17\" alt=\"negative 2\"></span></span>\n          </p>\n","ord":2},{"label":"D","content_html":"<p class=\"choice_paragraph \">The slope of line <span class=\"math_expression \"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/b3ed61300b239762a0f7bec1dc9a48ecd5e011d08d5338f426429aa3c459a067\" alt=\"l\"></span></span> is undefined.</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}}