{"id":"cb_question_bank:5933da62-0fb2-4ba7-87ab-2f4230eeef46","source_id":"cb_question_bank","source_item_id":"5933da62-0fb2-4ba7-87ab-2f4230eeef46","external_id":"83a73190-62d2-4465-82e0-b6794ffbddf6","ibn":null,"question_id":"3e9eaffc","program":"SAT","module":"math","domain_code":"H","domain":"Algebra","skill_code":"H.B.","skill":"Linear functions","difficulty":"M","score_band":4,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"Caleb used juice to make popsicles. The function f left parenthesis x right parenthesis equals minus 5 x plus 30 approximates the volume, in fluid ounces, of juice Caleb had remaining after making x popsicles. Which statement is the best interpretation of the y -intercept of the graph of y equals f left parenthesis x right parenthesis in the xy -plane in this context?","stimulus":"","stimulus_html":null,"stem_html":"<p style=\"text-align: left;\">Caleb used juice to make popsicles. The function&nbsp;<math alttext=\"f left parenthesis x right parenthesis equals minus 5 x plus 30\"><mi>f</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><mo>-</mo><mn>5</mn><mi>x</mi><mo>+</mo><mn>30</mn></math> approximates the volume, in fluid ounces, of juice Caleb had remaining after making <math alttext=\"x\"><mi>x</mi>\n</math> popsicles. Which statement is the best interpretation of the <em>y</em>-intercept of the graph of&nbsp;<math alttext=\"y equals f left parenthesis x right parenthesis\"><mi>y</mi><mo>=</mo><mi>f</mi><mfenced><mi>x</mi></mfenced></math> in the <em>xy</em>-plane in this context?</p>","rationale_html":"<p style=\"text-align: left;\">Choice C is correct. An equation that defines a linear function <math alttext=\"f\"><mi>f</mi>\n</math> can be written in the form <math alttext=\"f left parenthesis x right parenthesis equals m x plus b\"><mi>f</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><mi>m</mi><mi>x</mi><mo>+</mo><mi>b</mi></math>, where <math alttext=\"m\"><mi>m</mi>\n</math> represents the slope and <math alttext=\"b\"><mi>b</mi>\n</math> represents the <em>y</em>-intercept,&nbsp;<math alttext=\"left parenthesis 0 comma b right parenthesis\"><mfenced><mrow><mn>0</mn><mo>,</mo><mi>b</mi></mrow></mfenced></math>, of the line of&nbsp;<math alttext=\"y equals f left parenthesis x right parenthesis\"><mi>y</mi><mo>=</mo><mi>f</mi><mfenced><mi>x</mi></mfenced></math> in the <em>xy</em>-plane. The function <math alttext=\"f left parenthesis x right parenthesis equals minus 5 x plus 30\"><mi>f</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><mo>-</mo><mn>5</mn><mi>x</mi><mo>+</mo><mn>30</mn></math>&nbsp;is linear. Therefore, the graph of the given function <math alttext=\"y equals f left parenthesis x right parenthesis\"><mi>y</mi><mo>=</mo><mi>f</mi><mfenced><mi>x</mi></mfenced></math> in the <em>xy</em>-plane has a <em>y</em>-intercept of <math alttext=\"left parenthesis 0 comma 30 right parenthesis\"><mfenced><mrow><mn>0</mn><mo>,</mo><mn>30</mn></mrow></mfenced></math>. It’s given that <math alttext=\"f left parenthesis x right parenthesis\"><mi>f</mi><mfenced><mi>x</mi></mfenced></math> gives the approximate volume, in fluid ounces, of juice Caleb had remaining after making <math alttext=\"x\"><mi>x</mi>\n</math> popsicles. It follows that the <em>y</em>-intercept of <math alttext=\"left parenthesis 0 comma 30 right parenthesis\"><mfenced><mrow><mn>0</mn><mo>,</mo><mn>30</mn></mrow></mfenced></math> means that Caleb had approximately <math alttext=\"30\"><mn>30</mn>\n</math> fluid ounces of juice remaining after making <math alttext=\"0\"><mn>0</mn>\n</math> popsicles. In other words, Caleb had approximately <math alttext=\"30\"><mn>30</mn>\n</math> fluid ounces of juice when he began to make the popsicles.</p>\n<p>Choice A is incorrect. This is an interpretation of the slope, rather than the <em>y</em>-intercept, of the graph of <math alttext=\"y equals f left parenthesis x right parenthesis\"><mi>y</mi><mo>=</mo><mi>f</mi><mfenced><mi>x</mi></mfenced></math> in the <em>xy</em>-plane.</p>\n<p>Choice B is incorrect and may result from conceptual errors.</p>\n<p>Choice D is incorrect and may result from conceptual errors.</p>","correct_answer":["C"],"has_media":false,"has_mathml":true,"has_table":false,"source_created_at":"2023-08-02T20:25:59.811000+00:00","source_updated_at":"2023-08-02T20:25:59.811000+00:00","options":[{"label":"A","content_html":"<p style=\"text-align: left;\">Caleb used approximately <math alttext=\"5\"><mn>5</mn>\n</math> fluid ounces of juice for each popsicle.</p>","ord":0},{"label":"B","content_html":"<p style=\"text-align: left;\">Caleb had approximately <math alttext=\"5\"><mn>5</mn>\n</math> fluid ounces of juice when he began to make the popsicles.</p>","ord":1},{"label":"C","content_html":"<p style=\"text-align: left;\">Caleb had approximately <math alttext=\"30\"><mn>30</mn>\n</math> fluid ounces of juice when he began to make the popsicles.</p>","ord":2},{"label":"D","content_html":"<p style=\"text-align: left;\">Caleb used approximately <math alttext=\"30\"><mn>30</mn>\n</math> fluid ounces of juice for each popsicle.</p>","ord":3}],"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}}