{"id":"cb_question_bank:0d8bdd95-d411-40c9-a290-dcb5c5fb2bf4","source_id":"cb_question_bank","source_item_id":"0d8bdd95-d411-40c9-a290-dcb5c5fb2bf4","external_id":"451c1b50-026a-4bad-96b2-c090526934bf","ibn":null,"question_id":"5b8a8475","program":"SAT","module":"math","domain_code":"H","domain":"Algebra","skill_code":"H.C.","skill":"Linear equations in two variables","difficulty":"E","score_band":2,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"Line k is defined by y equals 3 x plus 15 . Line j is perpendicular to line k in the xy -plane. What is the slope of line j ?","stimulus":"","stimulus_html":null,"stem_html":"<p style=\"text-align: left;\">Line <math alttext=\"k\"><mi>k</mi>\n</math> is defined by <math alttext=\"y equals 3 x plus 15\"><mrow>\n\t<mi>y</mi>\n\t<mo>=</mo>\n\t<mrow>\n\t\t<mrow>\n\t\t\t<mn>3</mn>\n\t\t\t<mi>x</mi>\n\t\t</mrow>\n\t\t<mo>+</mo>\n\t\t<mn>15</mn>\n\t</mrow>\n</mrow>\n</math>. Line <math alttext=\"j\"><mi>j</mi>\n</math> is perpendicular to line <math alttext=\"k\"><mi>k</mi>\n</math> in the <em>xy</em>-plane. What is the slope of line <math alttext=\"j\"><mi>j</mi>\n</math>?</p>","rationale_html":"<p style=\"text-align: left;\">Choice A is correct. It's given that line <math alttext=\"j\"><mi>j</mi>\n</math> is perpendicular to line <math alttext=\"k\"><mi>k</mi>\n</math> in the <em>xy</em>-plane. It follows that the slope of line <math alttext=\"j\"><mi>j</mi>\n</math> is the opposite reciprocal of the slope of line <math alttext=\"k\"><mi>k</mi>\n</math>. The equation for line <math alttext=\"k\"><mi>k</mi>\n</math> is written in slope-intercept form <math alttext=\"y equals m x plus b\"><mrow>\n\t<mi>y</mi>\n\t<mo>=</mo>\n\t<mrow>\n\t\t<mrow>\n\t\t\t<mi>m</mi>\n\t\t\t<mi>x</mi>\n\t\t</mrow>\n\t\t<mo>+</mo>\n\t\t<mi>b</mi>\n\t</mrow>\n</mrow>\n</math>, where <math alttext=\"m\"><mi>m</mi>\n</math> is the slope of the line and&nbsp;<math alttext=\"b\"><mi>b</mi>\n</math> is the <em>y</em>-coordinate of the <em>y</em>-intercept of the line. It follows that the slope of line <math alttext=\"k\"><mi>k</mi>\n</math> is <math alttext=\"3\"><mn>3</mn>\n</math>. The opposite reciprocal of a number is <math alttext=\"negative 1\"><mo>-</mo><mn>1</mn>\n</math> divided by the number. Thus, the opposite reciprocal of <math alttext=\"3\"><mn>3</mn>\n</math> is <math alttext=\"negative one third\"><mo>-</mo><mfrac><mn>1</mn><mn>3</mn></mfrac></math>. Therefore, the slope of line <math alttext=\"j\"><mi>j</mi>\n</math> is <math alttext=\"negative one third\"><mrow>\n\t<mo>-</mo>\n\t<mfrac>\n\t\t<mn>1</mn>\n\t\t<mn>3</mn>\n\t</mfrac>\n</mrow>\n</math>.</p>\n<p style=\"text-align: left;\">Choice B is incorrect and may result from conceptual or calculation errors.</p>\n<p style=\"text-align: left;\">Choice C is incorrect and may result from conceptual or calculation errors.</p>\n<p style=\"text-align: left;\">Choice D is incorrect and may result from conceptual or calculation errors.</p>","correct_answer":["A"],"has_media":false,"has_mathml":true,"has_table":false,"source_created_at":"2023-08-02T20:25:59.816000+00:00","source_updated_at":"2023-08-02T20:25:59.816000+00:00","options":[{"label":"A","content_html":"<p><math alttext=\"negative one third\"><mrow>\n\t<mo>-</mo>\n\t<mfrac>\n\t\t<mn>1</mn>\n\t\t<mn>3</mn>\n\t</mfrac>\n</mrow>\n</math></p>","ord":0},{"label":"B","content_html":"<p><math alttext=\"negative one twelfth\"><mrow>\n\t<mo>-</mo>\n\t<mfrac>\n\t\t<mn>1</mn>\n\t\t<mn>12</mn>\n\t</mfrac>\n</mrow>\n</math></p>","ord":1},{"label":"C","content_html":"<p><math alttext=\"negative one eighteenth\"><mrow>\n\t<mo>-</mo>\n\t<mfrac>\n\t\t<mn>1</mn>\n\t\t<mn>18</mn>\n\t</mfrac>\n</mrow>\n</math></p>","ord":2},{"label":"D","content_html":"<p><math alttext=\"negative one forty fifth\"><mrow>\n\t<mo>-</mo>\n\t<mfrac>\n\t\t<mn>1</mn>\n\t\t<mn>45</mn>\n\t</mfrac>\n</mrow>\n</math></p>","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}}