{"id":"cb_question_bank:5b97ca84-0cb4-447e-8ae5-f99b13e13ca3","source_id":"cb_question_bank","source_item_id":"5b97ca84-0cb4-447e-8ae5-f99b13e13ca3","external_id":"63b423d6-d760-4ccc-974a-f9ad2904f1e9","ibn":null,"question_id":"db0107df","program":"SAT","module":"math","domain_code":"H","domain":"Algebra","skill_code":"H.C.","skill":"Linear equations in two variables","difficulty":"E","score_band":3,"answer_type":"spr","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"The y -intercept of the graph of 12 x plus 2 y equals 18 in the xy -plane is left parenthesis 0 comma y right parenthesis . What is the value of y ?","stimulus":"","stimulus_html":null,"stem_html":"<p style=\"text-align: left;\">The <em>y</em>-intercept of the graph of <math alttext=\"12 x plus 2 y equals 18\"><mrow>\n\t<mrow>\n\t\t<mrow>\n\t\t\t<mn>12</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>2</mn>\n\t\t\t<mi>y</mi>\n\t\t</mrow>\n\t</mrow>\n\t<mo>=</mo>\n\t<mn>18</mn>\n</mrow>\n</math> in the <em>xy</em>-plane is <math alttext=\"left parenthesis 0 comma y right parenthesis\"><mfenced><mrow><mn>0</mn><mo>,</mo><mi>y</mi></mrow></mfenced></math>. What is the value of <math alttext=\"y\"><mi>y</mi>\n</math>?</p>","rationale_html":"<p style=\"text-align: left;\">The correct answer is <math alttext=\"9\"><mn>9</mn>\n</math>. It's given that the <em>y</em>-intercept of the graph of <math alttext=\"12 x plus 2 y equals 18\"><mrow>\n\t<mrow>\n\t\t<mrow>\n\t\t\t<mn>12</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>2</mn>\n\t\t\t<mi>y</mi>\n\t\t</mrow>\n\t</mrow>\n\t<mo>=</mo>\n\t<mn>18</mn>\n</mrow>\n</math> in the <em>xy</em>-plane is <math alttext=\"left parenthesis 0 comma y right parenthesis\"><mfenced><mrow><mn>0</mn><mo>,</mo><mi>y</mi></mrow></mfenced></math>. Substituting <math alttext=\"0\"><mn>0</mn>\n</math> for <math alttext=\"x\"><mi>x</mi>\n</math> in the equation <math alttext=\"12 x plus 2 y equals 18\"><mrow>\n\t<mrow>\n\t\t<mrow>\n\t\t\t<mn>12</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>2</mn>\n\t\t\t<mi>y</mi>\n\t\t</mrow>\n\t</mrow>\n\t<mo>=</mo>\n\t<mn>18</mn>\n</mrow>\n</math> yields&nbsp;<math alttext=\"12 left parenthesis 0 right parenthesis plus 2 y equals 18\"><mn>12</mn><mfenced><mn>0</mn></mfenced><mo>+</mo><mn>2</mn><mi>y</mi><mo>=</mo><mn>18</mn></math>, or <math alttext=\"2 y equals 18\"><mrow>\n\t<mrow>\n\t\t<mn>2</mn>\n\t\t<mi>y</mi>\n\t</mrow>\n\t<mo>=</mo>\n\t<mn>18</mn>\n</mrow>\n</math>. Dividing both sides of this equation by <math alttext=\"2\"><mn>2</mn>\n</math> yields <math alttext=\"y equals 9\"><mrow>\n\t<mi>y</mi>\n\t<mo>=</mo>\n\t<mn>9</mn>\n</mrow>\n</math>. Therefore, the value of <math alttext=\"y\"><mi>y</mi>\n</math> is <math alttext=\"9\"><mn>9</mn>\n</math>.</p>","correct_answer":["9"],"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}}