{"id":"cb_question_bank:013b49a8-e0e3-4cde-8913-5016b184fb62","source_id":"cb_question_bank","source_item_id":"013b49a8-e0e3-4cde-8913-5016b184fb62","external_id":"65ac5dc5-af25-4ecf-8562-a346047750a6","ibn":null,"question_id":"002dba45","program":"SAT","module":"math","domain_code":"H","domain":"Algebra","skill_code":"H.C.","skill":"Linear equations in two variables","difficulty":"M","score_band":5,"answer_type":"spr","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"Line k is defined by y equals minus StartFraction 17 Over 3 EndFraction x plus 5 . 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>Line <math alttext=\"k\"><mi>k</mi>\n</math> is defined by <math alttext=\"y equals minus StartFraction 17 Over 3 EndFraction x plus 5\"><mi>y</mi><mo>=</mo><mo>-</mo><mfrac><mrow><mn>17</mn></mrow><mrow><mn>3</mn></mrow></mfrac><mi>x</mi><mo>+</mo><mrow><mn>5</mn></mrow></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;\">The correct answer is <math alttext=\"three seventeenths\"><mfrac>\n\t<mn>3</mn>\n\t<mn>17</mn>\n</mfrac>\n</math>. 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. This means that the slope of line <math alttext=\"j\"><mi>j</mi>\n</math> is the negative reciprocal of the slope of line <math alttext=\"k\"><mi>k</mi>\n</math>. The equation of line <math alttext=\"k\"><mi>k</mi>\n</math>, <math alttext=\"y equals minus StartFraction 17 Over 3 EndFraction x plus 5\"><mi>y</mi><mo>=</mo><mo>-</mo><mfrac><mn>17</mn><mn>3</mn></mfrac><mi>x</mi><mo>+</mo><mn>5</mn></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 <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=\"negative StartFraction 17 Over 3 EndFraction\"><mrow>\n\t<mo>-</mo>\n\t<mfrac>\n\t\t<mn>17</mn>\n\t\t<mn>3</mn>\n\t</mfrac>\n</mrow>\n</math>. The negative reciprocal of a number is <math alttext=\"negative 1\"><mo>-</mo><mn>1</mn>\n</math> divided by the number. Therefore, the negative reciprocal of <math alttext=\"negative StartFraction 17 Over 3 EndFraction\"><mrow>\n\t<mo>-</mo>\n\t<mfrac>\n\t\t<mn>17</mn>\n\t\t<mn>3</mn>\n\t</mfrac>\n</mrow>\n</math> is <math alttext=\"StartStartFraction negative 1 OverOver negative StartFraction 17 Over 3 EndFraction EndEndFraction\"><mfrac><mrow><mo>-</mo><mn>1</mn></mrow><mrow><mo>-</mo><mstyle displaystyle=\"true\"><mfrac><mn>17</mn><mn>3</mn></mfrac></mstyle></mrow></mfrac></math>, or <math alttext=\"three seventeenths\"><mfrac>\n\t<mn>3</mn>\n\t<mn>17</mn>\n</mfrac>\n</math>. Thus, the slope of line <math alttext=\"j\"><mi>j</mi>\n</math> is <math alttext=\"three seventeenths\"><mfrac>\n\t<mn>3</mn>\n\t<mn>17</mn>\n</mfrac>\n</math>. Note that 3/17, .1764, .1765, and 0.176 are examples of ways to enter a correct answer.</p>","correct_answer":[".1764",".1765","3/17"],"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":[],"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}}