{"id":"cb_question_bank:75ca26a8-3aac-4d1b-b195-625680e60370","source_id":"cb_question_bank","source_item_id":"75ca26a8-3aac-4d1b-b195-625680e60370","external_id":"c6aceeba-b507-44a2-bc31-9beb10096c93","ibn":null,"question_id":"94b48cbf","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":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"The graph of 7 x plus 2 y equals negative 31 in the x y -plane has an x -intercept at left parenthesis a comma 0 right parenthesis and a y -intercept at left parenthesis 0 comma b right parenthesis , where a and b are constants. What is the value of StartFraction b Over a EndFraction ?","stimulus":"","stimulus_html":null,"stem_html":"

The graph of \n\t\n\t\t\n\t\t\t7\n\t\t\tx\n\t\t\n\t\t+\n\t\t\n\t\t\t2\n\t\t\ty\n\t\t\n\t\n\t=\n\t-31\n\n in the \n\tx\n\ty\n\n-plane has an x\n-intercept at (a\n, 0\n) and a y\n-intercept at (0\n, b\n), where a\n and b\n are constants. What is the value of \n\t\tb\n\t\ta\n\t\n?

","rationale_html":"

Choice D is correct. The x-coordinate a\n of the x-intercept a,0 can be found by substituting 0\n for y\n in the given equation, which gives 7x+20=-31, or 7x=-31. Dividing both sides of this equation by 7\n yields x=-317. Therefore, the value of a\n is -317. The y-coordinate b\n of the y-intercept 0,b can be found by substituting 0\n for x\n in the given equation, which gives 70+2y=-31, or 2y=-31. Dividing both sides of this equation by 2\n yields y=-312. Therefore, the value of b\n is -312. It follows that the value of \n\t\n\t\tb\n\t\ta\n\t\n\n is -312-317, which is equivalent to 312731, or \n\t7\n\t2\n\n.

\n

Choice A is incorrect and may result from conceptual or calculation errors.

\n

Choice B is incorrect and may result from conceptual or calculation errors.

\n

Choice C is incorrect and may result from conceptual or calculation errors.

","correct_answer":["D"],"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":[{"label":"A","content_html":"

\n\t-\n\t\n\t\t7\n\t\t2\n\t\n\n

","ord":0},{"label":"B","content_html":"

\n\t-\n\t\n\t\t2\n\t\t7\n\t\n\n

","ord":1},{"label":"C","content_html":"

\n\t2\n\t7\n\n

","ord":2},{"label":"D","content_html":"

\n\t7\n\t2\n\n

","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}}