{"id":"cb_question_bank:dc43dcbf-4d99-43e8-9baa-5075708e49e1","source_id":"cb_question_bank","source_item_id":"dc43dcbf-4d99-43e8-9baa-5075708e49e1","external_id":"eb64b8f6-731a-4137-9ed2-358ab19f106c","ibn":null,"question_id":"6f6dfe3e","program":"SAT","module":"math","domain_code":"H","domain":"Algebra","skill_code":"H.C.","skill":"Linear equations in two variables","difficulty":"M","score_band":5,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"x y negative 6 n plus 184 negative 3 n plus 92 0 n The table shows three values of x and their corresponding values of y , where n is a constant, for the linear relationship between x and y . What is the slope of the line that represents this relationship in the xy -plane?","stimulus":"","stimulus_html":null,"stem_html":"
\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
x\ny\n
-6\n\n\tn\n\t+\n\t184\n\n
-3\n\n\tn\n\t+\n\t92\n\n
0\nn\n
\n

The table shows three values of x\n and their corresponding values of y\n, where n\n is a constant, for the linear relationship between x\n and y\n. What is the slope of the line that represents this relationship in the xy-plane?

","rationale_html":"

Choice A is correct. The slope, m\n, of a line in the xy-plane can be found using two points on the line, x1,y1 and x2,y2, and the slope formula m=y2-y1x2-x1. Based on the given table, the line representing the relationship between x\n and y\n in the xy-plane passes through the points -6,n+184, -3,n+92, and 0,n, where n\n is a constant. Substituting two of these points, -3,n+92 and 0,n, for x1,y1 and x2,y2, respectively, in the slope formula yields m=n-n+920--3, which is equivalent to m=n-n-920+3, or m=-923. Therefore, the slope of the line that represents this relationship in the xy-plane is \n\t-\n\t\n\t\t92\n\t\t3\n\t\n\n.

\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.

\n

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

","correct_answer":["A"],"has_media":false,"has_mathml":true,"has_table":true,"source_created_at":"2023-08-02T20:25:59.815000+00:00","source_updated_at":"2023-08-02T20:25:59.815000+00:00","options":[{"label":"A","content_html":"

\n\t-\n\t\n\t\t92\n\t\t3\n\t\n\n

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

\n\t-\n\t\n\t\t3\n\t\t92\n\t\n\n

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

n+92-3

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

2n-923

","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}}