{"id":"cb_question_bank:8eff5bc0-b422-49de-a1a1-f37c3f79df07","source_id":"cb_question_bank","source_item_id":"8eff5bc0-b422-49de-a1a1-f37c3f79df07","external_id":"54986bed-7fc7-4f46-a3c6-d49d4fe54080","ibn":null,"question_id":"ba79f10f","program":"SAT","module":"math","domain_code":"H","domain":"Algebra","skill_code":"H.C.","skill":"Linear equations in two variables","difficulty":"E","score_band":3,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"x y 0 18 1 13 2 8 The table shows three values of x and their corresponding values of y . There is a linear relationship between x and y . Which of the following equations represents this relationship?","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
0\n18\n
1\n13\n
2\n8\n
\n

The table shows three values of x\n and their corresponding values of y\n. There is a linear relationship between x\n and y\n. Which of the following equations represents this relationship?

","rationale_html":"

Choice D is correct. A linear relationship can be represented by an equation of the form \n\ty\n\t=\n\t\n\t\t\n\t\t\tm\n\t\t\tx\n\t\t\n\t\t+\n\t\tb\n\t\n\n, where m\n and b\n are constants. It’s given in the table that when \n\tx\n\t=\n\t0\n\n, \n\ty\n\t=\n\t18\n\n. Substituting 0\n for x\n and 18\n for y\n in \n\ty\n\t=\n\t\n\t\t\n\t\t\tm\n\t\t\tx\n\t\t\n\t\t+\n\t\tb\n\t\n\n yields 18=m0+b, or \n\t18\n\t=\n\tb\n\n. Substituting 18\n for b\n in the equation \n\ty\n\t=\n\t\n\t\t\n\t\t\tm\n\t\t\tx\n\t\t\n\t\t+\n\t\tb\n\t\n\n yields \n\ty\n\t=\n\t\n\t\t\n\t\t\tm\n\t\t\tx\n\t\t\n\t\t+\n\t\t18\n\t\n\n. It’s also given in the table that when \n\tx\n\t=\n\t1\n\n, \n\ty\n\t=\n\t13\n\n. Substituting 1\n for x\n and 13\n for y\n in the equation \n\ty\n\t=\n\t\n\t\t\n\t\t\tm\n\t\t\tx\n\t\t\n\t\t+\n\t\t18\n\t\n\n yields 13=m1+18, or \n\t13\n\t=\n\t\n\t\tm\n\t\t+\n\t\t18\n\t\n\n. Subtracting 18\n from both sides of this equation yields \n\t-5\n\t=\n\tm\n\n. Therefore, the equation \n\ty\n\t=\n\t\n\t\t\n\t\t\t-\n\t\t\t5\n\t\t\tx\n\t\t\n\t\t+\n\t\t18\n\t\n\n represents the relationship between x\n and y\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":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\ty\n\t=\n\t\n\t\t\n\t\t\t18\n\t\t\tx\n\t\t\n\t\t+\n\t\t13\n\t\n\n

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

\n\ty\n\t=\n\t\n\t\t\n\t\t\t18\n\t\t\tx\n\t\t\n\t\t+\n\t\t18\n\t\n\n

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

\n\ty\n\t=\n\t\n\t\t\n\t\t\t-\n\t\t\t5\n\t\t\tx\n\t\t\n\t\t+\n\t\t13\n\t\n\n

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

\n\ty\n\t=\n\t\n\t\t\n\t\t\t-\n\t\t\t5\n\t\t\tx\n\t\t\n\t\t+\n\t\t18\n\t\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}}