{"id":"cb_question_bank:46430e32-da44-47d0-9533-7e8cffa94671","source_id":"cb_question_bank","source_item_id":"46430e32-da44-47d0-9533-7e8cffa94671","external_id":"b64bd9d3-56b1-45f6-b301-f29dfd4eb579","ibn":null,"question_id":"f7e39fe9","program":"SAT","module":"math","domain_code":"H","domain":"Algebra","skill_code":"H.B.","skill":"Linear functions","difficulty":"M","score_band":4,"answer_type":"spr","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"x 10 15 20 25 f left parenthesis x right parenthesis 82 137 192 247 The table shows four values of x and their corresponding values of f left parenthesis x right parenthesis . There is a linear relationship between x and f left parenthesis x right parenthesis that is defined by the equation f left parenthesis x right parenthesis equals m x minus 28 , where m is a constant. What is the value of m ?","stimulus":"","stimulus_html":null,"stem_html":"<table style=\"border-collapse: collapse; width: 42.4581%; border-color: #000000; border-style: solid; margin-left: auto; margin-right: auto; height: 41px;\" border=\"1\">\n<tbody>\n<tr>\n<th style=\"width: 17.4264%; text-align: center;\" scope=\"row\"><math alttext=\"x\"><mi>x</mi>\n</math></th>\n<td style=\"width: 17.4264%; text-align: center;\"><math alttext=\"10\"><mn>10</mn>\n</math></td>\n<td style=\"width: 17.4264%; text-align: center;\"><math alttext=\"15\"><mn>15</mn>\n</math></td>\n<td style=\"width: 17.4264%; text-align: center;\"><math alttext=\"20\"><mn>20</mn>\n</math></td>\n<td style=\"width: 17.4264%; text-align: center;\"><math alttext=\"25\"><mn>25</mn>\n</math></td>\n</tr>\n<tr>\n<th style=\"width: 17.4264%; text-align: center;\" scope=\"row\"><math alttext=\"f left parenthesis x right parenthesis\"><mi>f</mi><mfenced><mi>x</mi></mfenced></math></th>\n<td style=\"width: 17.4264%; text-align: center;\"><math alttext=\"82\"><mn>82</mn>\n</math></td>\n<td style=\"width: 17.4264%; text-align: center;\"><math alttext=\"137\"><mn>137</mn>\n</math></td>\n<td style=\"width: 17.4264%; text-align: center;\"><math alttext=\"192\"><mn>192</mn>\n</math></td>\n<td style=\"width: 17.4264%; text-align: center;\"><math alttext=\"247\"><mn>247</mn>\n</math></td>\n</tr>\n</tbody>\n</table>\n<p style=\"text-align: left;\">The table shows four values of <math alttext=\"x\"><mi>x</mi>\n</math> and their corresponding values of <math alttext=\"f left parenthesis x right parenthesis\"><mi>f</mi><mfenced><mi>x</mi></mfenced></math>. There is a linear relationship between <math alttext=\"x\"><mi>x</mi>\n</math>&nbsp;and <math alttext=\"f left parenthesis x right parenthesis\"><mi>f</mi><mfenced><mi>x</mi></mfenced></math> that is defined by the equation <math alttext=\"f left parenthesis x right parenthesis equals m x minus 28\"><mi>f</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><mi>m</mi><mi>x</mi><mo>-</mo><mrow><mn>28</mn></mrow></math>, where <math alttext=\"m\"><mi>m</mi>\n</math> is a constant. What is the value of <math alttext=\"m\"><mi>m</mi>\n</math>?</p>","rationale_html":"<p style=\"text-align: left;\">The correct answer is <math alttext=\"11\"><mn>11</mn>\n</math>. It's given that&nbsp;<math alttext=\"f left parenthesis x right parenthesis\"><mi>f</mi><mfenced><mi>x</mi></mfenced></math> is defined by the equation <math alttext=\"f left parenthesis x right parenthesis equals m x minus 28\"><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mi>m</mi><mi>x</mi><mo>-</mo><mn>28</mn></math>, where <math alttext=\"m\"><mi>m</mi>\n</math> is a constant. It's also given in the table that when <math alttext=\"x equals 10\"><mrow>\n\t<mi>x</mi>\n\t<mo>=</mo>\n\t<mn>10</mn>\n</mrow>\n</math>, <math alttext=\"f left parenthesis x right parenthesis equals 82\"><mi>f</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><mn>82</mn></math>. Substituting <math alttext=\"10\"><mn>10</mn>\n</math> for <math alttext=\"x\"><mi>x</mi>\n</math> and <math alttext=\"82\"><mn>82</mn>\n</math> for <math alttext=\"f left parenthesis x right parenthesis\"><mi>f</mi><mfenced><mi>x</mi></mfenced></math> in the equation <math alttext=\"f left parenthesis x right parenthesis equals m x minus 28\"><mi>f</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><mi>m</mi><mi>x</mi><mo>-</mo><mn>28</mn></math> yields,&nbsp;<math alttext=\"82 equals m left parenthesis 10 right parenthesis minus 28\"><mn>82</mn><mo>=</mo><mi>m</mi><mfenced><mn>10</mn></mfenced><mo>-</mo><mn>28</mn></math>. Adding <math alttext=\"28\"><mn>28</mn>\n</math> to both sides of this equation yields <math alttext=\"110 equals 10 m\"><mrow>\n\t<mn>110</mn>\n\t<mo>=</mo>\n\t<mrow>\n\t\t<mn>10</mn>\n\t\t<mi>m</mi>\n\t</mrow>\n</mrow>\n</math>. Dividing both sides of this equation by <math alttext=\"10\"><mn>10</mn>\n</math> yields <math alttext=\"11 equals m\"><mrow>\n\t<mn>11</mn>\n\t<mo>=</mo>\n\t<mi>m</mi>\n</mrow>\n</math>.&nbsp;Therefore, the value of <math alttext=\"m\"><mi>m</mi>\n</math> is <math alttext=\"11\"><mn>11</mn>\n</math>.</p>","correct_answer":["11"],"has_media":false,"has_mathml":true,"has_table":true,"source_created_at":"2023-08-02T20:25:59.811000+00:00","source_updated_at":"2023-08-02T20:25:59.811000+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}}