{"id":"cb_question_bank:a1e2d08e-4fc4-45ea-8bbb-a996a14a0b10","source_id":"cb_question_bank","source_item_id":"a1e2d08e-4fc4-45ea-8bbb-a996a14a0b10","external_id":"02e0a325-790e-4a20-956c-c646b0e6a227","ibn":null,"question_id":"cc3e9528","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":"spr","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"The graph of 9 x minus 10 y equals 19 is translated down 4 units in the xy -plane. What is the x -coordinate of the x -intercept of the resulting graph?","stimulus":"","stimulus_html":null,"stem_html":"<p style=\"text-align: left;\">The graph of <math alttext=\"9 x minus 10 y equals 19\"><mrow><mn>9</mn></mrow><mi>x</mi><mo>-</mo><mrow><mn>10</mn></mrow><mi>y</mi><mo>=</mo><mrow><mn>19</mn></mrow></math> is translated down <math alttext=\"4\"><mn>4</mn>\n</math> units in the <em>xy</em>-plane. What is the <em>x</em>-coordinate of the <em>x</em>-intercept of the resulting graph?</p>","rationale_html":"<p style=\"text-align: left;\">The correct answer is <math alttext=\"StartFraction 59 Over 9 EndFraction\"><mfrac>\n\t<mn>59</mn>\n\t<mn>9</mn>\n</mfrac>\n</math>. When the graph of an equation in the form <math alttext=\"upper A x plus upper B y equals upper C\"><mrow>\n\t<mrow>\n\t\t<mrow>\n\t\t\t<mi>A</mi>\n\t\t\t<mi>x</mi>\n\t\t</mrow>\n\t\t<mo>+</mo>\n\t\t<mrow>\n\t\t\t<mi>B</mi>\n\t\t\t<mi>y</mi>\n\t\t</mrow>\n\t</mrow>\n\t<mo>=</mo>\n\t<mi>C</mi>\n</mrow>\n</math>, where <math alttext=\"upper A\"><mi>A</mi>\n</math>, <math alttext=\"upper B\"><mi>B</mi>\n</math>, and <math alttext=\"upper C\"><mi>C</mi>\n</math> are constants, is translated down <math alttext=\"k\"><mi>k</mi>\n</math> units in the&nbsp;<em>xy</em>-plane, the resulting graph can be represented by the equation&nbsp;<math alttext=\"upper A x plus upper B left parenthesis y plus k right parenthesis equals upper C\"><mi>A</mi><mi>x</mi><mo>+</mo><mi>B</mi><mfenced><mrow><mi>y</mi><mo>+</mo><mi>k</mi></mrow></mfenced><mo>=</mo><mi>C</mi></math>. It’s given that the graph of <math alttext=\"9 x minus 10 y equals 19\"><mrow>\n\t<mrow>\n\t\t<mrow>\n\t\t\t<mn>9</mn>\n\t\t\t<mi>x</mi>\n\t\t</mrow>\n\t\t<mo>-</mo>\n\t\t<mrow>\n\t\t\t<mn>10</mn>\n\t\t\t<mi>y</mi>\n\t\t</mrow>\n\t</mrow>\n\t<mo>=</mo>\n\t<mn>19</mn>\n</mrow>\n</math> is translated down <math alttext=\"4\"><mn>4</mn>\n</math> units in the <em>xy</em>-plane. Therefore, the resulting graph can be represented by the equation <math alttext=\"9 x minus 10 left parenthesis y plus 4 right parenthesis equals 19\"><mn>9</mn><mi>x</mi><mo>-</mo><mn>10</mn><mfenced><mrow><mi>y</mi><mo>+</mo><mn>4</mn></mrow></mfenced><mo>=</mo><mn>19</mn></math>, or&nbsp;<math alttext=\"9 x minus 10 y minus 40 equals 19\"><mn>9</mn><mi>x</mi><mo>-</mo><mn>10</mn><mi>y</mi><mo>-</mo><mn>40</mn><mo>=</mo><mn>19</mn></math>. Adding <math alttext=\"40\"><mn>40</mn>\n</math> to both sides of this equation yields <math alttext=\"9 x minus 10 y equals 59\"><mrow>\n\t<mrow>\n\t\t<mrow>\n\t\t\t<mn>9</mn>\n\t\t\t<mi>x</mi>\n\t\t</mrow>\n\t\t<mo>-</mo>\n\t\t<mrow>\n\t\t\t<mn>10</mn>\n\t\t\t<mi>y</mi>\n\t\t</mrow>\n\t</mrow>\n\t<mo>=</mo>\n\t<mn>59</mn>\n</mrow>\n</math>. The <em>x</em>-coordinate of the <em>x</em>-intercept of the graph of an equation in the <em>xy</em>-plane is the value of <math alttext=\"x\"><mi>x</mi>\n</math> in the equation when <math alttext=\"y equals 0\"><mrow>\n\t<mi>y</mi>\n\t<mo>=</mo>\n\t<mn>0</mn>\n</mrow>\n</math>. Substituting <math alttext=\"0\"><mn>0</mn>\n</math> for <math alttext=\"y\"><mi>y</mi>\n</math> in the equation <math alttext=\"9 x minus 10 y equals 59\"><mrow>\n\t<mrow>\n\t\t<mrow>\n\t\t\t<mn>9</mn>\n\t\t\t<mi>x</mi>\n\t\t</mrow>\n\t\t<mo>-</mo>\n\t\t<mrow>\n\t\t\t<mn>10</mn>\n\t\t\t<mi>y</mi>\n\t\t</mrow>\n\t</mrow>\n\t<mo>=</mo>\n\t<mn>59</mn>\n</mrow>\n</math> yields <math alttext=\"9 x minus 10 left parenthesis 0 right parenthesis equals 59\"><mn>9</mn><mi>x</mi><mo>-</mo><mn>10</mn><mfenced><mn>0</mn></mfenced><mo>=</mo><mn>59</mn></math>, or <math alttext=\"9 x equals 59\"><mrow>\n\t<mrow>\n\t\t<mn>9</mn>\n\t\t<mi>x</mi>\n\t</mrow>\n\t<mo>=</mo>\n\t<mn>59</mn>\n</mrow>\n</math>. Dividing both sides of this equation by <math alttext=\"9\"><mn>9</mn>\n</math> yields <math alttext=\"x equals StartFraction 59 Over 9 EndFraction\"><mrow>\n\t<mi>x</mi>\n\t<mo>=</mo>\n\t<mfrac>\n\t\t<mn>59</mn>\n\t\t<mn>9</mn>\n\t</mfrac>\n</mrow>\n</math>. Therefore, the <em>x</em>-coordinate of the <em>x</em>-intercept of the resulting graph is <math alttext=\"StartFraction 59 Over 9 EndFraction\"><mfrac>\n\t<mn>59</mn>\n\t<mn>9</mn>\n</mfrac>\n</math>. Note that 59/9, 6.555, and 6.556 are examples of ways to enter a correct answer.</p>","correct_answer":["59/9","6.555","6.556"],"has_media":false,"has_mathml":true,"has_table":false,"source_created_at":"2023-08-02T20:25:59.814000+00:00","source_updated_at":"2023-08-02T20:25:59.814000+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}}