{"id":"cb_question_bank:ec5ade92-ea7e-4adf-a4ef-68d0fbe09a35","source_id":"cb_question_bank","source_item_id":"ec5ade92-ea7e-4adf-a4ef-68d0fbe09a35","external_id":"70799514-1e68-4ec1-9002-6b0e1165cbb0","ibn":null,"question_id":"3ce92ce8","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":"f left parenthesis x right parenthesis equals 2 x plus 3 For the given function f , the graph of y equals f left parenthesis x right parenthesis in the xy -plane is parallel to line j . What is the slope of line j ?","stimulus":"","stimulus_html":null,"stem_html":"<p style=\"text-align: center;\"><math alttext=\"f left parenthesis x right parenthesis equals 2 x plus 3\"><mi>f</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><mrow><mn>2</mn></mrow><mi>x</mi><mo>+</mo><mrow><mn>3</mn></mrow></math></p>\n<p>For the given function <math alttext=\"f\"><mi>f</mi>\n</math>, 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 is parallel to line <math alttext=\"j\"><mi>j</mi>\n</math>. What is the slope of line <math alttext=\"j\"><mi>j</mi>\n</math>?</p>","rationale_html":"<p style=\"text-align: left;\">The correct answer is <math alttext=\"2\"><mn>2</mn>\n</math>. It’s given that function <math alttext=\"f\"><mi>f</mi>\n</math> is defined by <math alttext=\"f left parenthesis x right parenthesis equals 2 x plus 3\"><mi>f</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><mn>2</mn><mi>x</mi><mo>+</mo><mn>3</mn></math>. Therefore, the equation representing 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 is <math alttext=\"y equals 2 x plus 3\"><mi>y</mi><mo>=</mo><mn>2</mn><mi>x</mi><mo>+</mo><mn>3</mn></math>, and the graph is a line. For a linear equation in the form <math alttext=\"y equals m x plus b\"><mi>y</mi><mo>=</mo><mi>m</mi><mi>x</mi><mo>+</mo><mi>b</mi></math>, <math alttext=\"m\"><mi>m</mi>\n</math> represents the slope of the line. Since the value of <math alttext=\"m\"><mi>m</mi>\n</math> in the equation <math alttext=\"y equals 2 x plus 3\"><mi>y</mi><mo>=</mo><mn>2</mn><mi>x</mi><mo>+</mo><mn>3</mn></math> is <math alttext=\"2\"><mn>2</mn>\n</math>, the slope of the line defined by function <math alttext=\"f\"><mi>f</mi>\n</math> is <math alttext=\"2\"><mn>2</mn>\n</math>. It's given that line <math alttext=\"j\"><mi>j</mi>\n</math> is parallel to the line defined by function <math alttext=\"f\"><mi>f</mi>\n</math>. The slopes of parallel lines are equal. Therefore, the slope of line <math alttext=\"j\"><mi>j</mi>\n</math> is also <math alttext=\"2\"><mn>2</mn>\n</math>.</p>","correct_answer":["2"],"has_media":false,"has_mathml":true,"has_table":false,"source_created_at":"2023-08-02T20:25:59.812000+00:00","source_updated_at":"2023-08-02T20:25:59.812000+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}}