{"id":"cb_question_bank:02672cb2-7340-4344-8dc8-257d5159823b","source_id":"cb_question_bank","source_item_id":"02672cb2-7340-4344-8dc8-257d5159823b","external_id":"83c4d031-e8f1-4415-8c6c-33d11d65e85b","ibn":null,"question_id":"3008cfc3","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":"spr","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"x y k 13 k plus 7 negative 15 The table gives the coordinates of two points on a line in the xy -plane. The y -intercept of the line is left parenthesis k minus 5 comma b right parenthesis , where k and b are constants. What is the value of b ?","stimulus":"","stimulus_html":null,"stem_html":"
\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
x\ny\n
k\n13\n
\n\tk\n\t+\n\t7\n\n-15\n
\n

The table gives the coordinates of two points on a line in the xy-plane. The y-intercept of the line is k-5,b, where k\n and b\n are constants. What is the value of b\n?

","rationale_html":"

The correct answer is 33\n. It’s given in the table that the coordinates of two points on a line in the xy-plane are (k,13) and (k+7,-15). The y-intercept is another point on the line. The slope computed using any pair of points from the line will be the same. The slope of a line, m\n, between any two points, x1,y1 and x2,y2, on the line can be calculated using the slope formula, m=y2-y1x2-x1. It follows that the slope of the line with the given points from the table, (k,13) and (k+7,-15), is m=-15-13k+7-k, which is equivalent to m=-287, or m=-4. It's given that the y-intercept of the line is (k-5,b). Substituting -4\n for m\n and the coordinates of the points (k-5,b) and (k,13) into the slope formula yields -4=13-bk-k-5, which is equivalent to -4=13-bk-k+5, or -4=13-b5. Multiplying both sides of this equation by 5\n yields -20=13-b. Subtracting 13\n from both sides of this equation yields -33=-b. Dividing both sides of this equation by -1 yields b=33. Therefore, the value of b\n is 33\n.

","correct_answer":["33"],"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":[],"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}}