{"id":"cb_question_bank:e82d0397-dca9-4207-8ea4-8aad72039052","source_id":"cb_question_bank","source_item_id":"e82d0397-dca9-4207-8ea4-8aad72039052","external_id":"55d9f495-d3f8-4300-aadb-4beb4b5365d2","ibn":null,"question_id":"9ed4c1a2","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":"What is the slope of the graph of y equals one fourth left parenthesis 27 x plus 15 right parenthesis plus 7 x in the xy -plane?","stimulus":"","stimulus_html":null,"stem_html":"<p style=\"text-align: left;\">What is the slope of the graph of <math alttext=\"y equals one fourth left parenthesis 27 x plus 15 right parenthesis plus 7 x\"><mi>y</mi><mo>=</mo><mfrac><mn>1</mn><mrow><mn>4</mn></mrow></mfrac><mfenced><mrow><mrow><mn>27</mn></mrow><mi>x</mi><mo>+</mo><mrow><mn>15</mn></mrow></mrow></mfenced><mo>+</mo><mrow><mn>7</mn></mrow><mi>x</mi></math>&nbsp;in the&nbsp;<em>xy</em>-plane?</p>","rationale_html":"<p style=\"text-align: left;\">The correct answer is&nbsp;<math alttext=\"StartFraction 55 Over 4 EndFraction\"><mfrac><mn>55</mn><mn>4</mn></mfrac></math>. In the <em>xy</em>-plane, the graph of an equation in the 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> and <math alttext=\"b\"><mi>b</mi>\n</math> are constants, has a slope of <math alttext=\"m\"><mi>m</mi>\n</math> and a <em>y</em>-intercept of <math alttext=\"left parenthesis 0 comma b right parenthesis\"><mfenced><mrow><mn>0</mn><mo>,</mo><mi>b</mi></mrow></mfenced></math>. Applying the distributive property to the right-hand side of the given equation yields <math alttext=\"y equals StartFraction 27 Over 4 EndFraction x plus StartFraction 15 Over 4 EndFraction plus 7 x\"><mi>y</mi><mo>=</mo><mfrac><mn>27</mn><mn>4</mn></mfrac><mi>x</mi><mo>+</mo><mfrac><mn>15</mn><mn>4</mn></mfrac><mo>+</mo><mn>7</mn><mi>x</mi></math>. Combining like terms yields&nbsp;<math alttext=\"y equals StartFraction 55 Over 4 EndFraction x plus StartFraction 15 Over 4 EndFraction\"><mi>y</mi><mo>=</mo><mfrac><mn>55</mn><mn>4</mn></mfrac><mi>x</mi><mo>+</mo><mfrac><mn>15</mn><mn>4</mn></mfrac></math>. This equation is in the 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 equals StartFraction 55 Over 4 EndFraction\"><mrow>\n\t<mi>m</mi>\n\t<mo>=</mo>\n\t<mfrac>\n\t\t<mn>55</mn>\n\t\t<mn>4</mn>\n\t</mfrac>\n</mrow>\n</math> and <math alttext=\"b equals StartFraction 15 Over 4 EndFraction\"><mrow>\n\t<mi>b</mi>\n\t<mo>=</mo>\n\t<mfrac>\n\t\t<mn>15</mn>\n\t\t<mn>4</mn>\n\t</mfrac>\n</mrow>\n</math>. It follows that the slope of the graph of <math alttext=\"y equals one fourth left parenthesis 27 x plus 15 right parenthesis plus 7 x\"><mi>y</mi><mo>=</mo><mfrac><mn>1</mn><mn>4</mn></mfrac><mfenced><mrow><mn>27</mn><mi>x</mi><mo>+</mo><mn>15</mn></mrow></mfenced><mo>+</mo><mn>7</mn><mi>x</mi></math> in the&nbsp;<em>xy</em>-plane is&nbsp;<math alttext=\"StartFraction 55 Over 4 EndFraction\"><mfrac><mn>55</mn><mn>4</mn></mfrac></math>. Note that 55/4 and 13.75 are examples of ways to enter a correct answer.</p>","correct_answer":["13.75","55/4"],"has_media":false,"has_mathml":true,"has_table":false,"source_created_at":"2023-08-02T20:25:59.815000+00:00","source_updated_at":"2023-08-02T20:25:59.815000+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}}