{"id":"cb_practice_pdf:t4-math-m1-q15","source_id":"cb_practice_pdf","source_item_id":"t4-math-m1-q15","external_id":null,"ibn":null,"question_id":null,"program":"SAT","module":"math","domain_code":null,"domain":null,"skill_code":null,"skill":null,"difficulty":null,"score_band":null,"answer_type":"mcq","answer_source":"rationale","layout_warning":null,"form_id":"cb_practice_pdf:test-4","module_number":1,"position":15,"stem":"Line t in the xy-plane has a slope of − 1/3 and passes (9, 10) through the point. Which equation defines line t?","stimulus":"","stimulus_html":null,"stem_html":"<p>Line t in the xy-plane has a slope of − 1/3 and passes (9, 10) through the point. Which equation defines line t?</p>","rationale_html":"<p>Choice D is correct. The equation that defines line t in the xy-plane can be = + written in slope-intercept form y mx b, where m is the slope of line t and ( ) -1 =-1 0, b is its y-intercept. It’s given that line t has a slope of . Therefore, m . 3 3 -1 = + =- 1+ Substituting for m in the equation y mx b yields y x b, or 3 3 =- + x ( ) y b. It’s also given that line t passes through the point 9, 10 . 3 =- + x Substituting 9 for x and 10 for y in the equation y b yields 3 =-9+ =- + 10 b, or 10 3 b. Adding 3 to both sides of this equation yields 3 = =- + x =-x + 13 b. Substituting 13 for b in the equation y b yields y 13. 3 3 Choice A is incorrect and may result from conceptual or calculation errors. -1 Choice B is incorrect. This equation defines a line that has a slope of 9, not , ( ) ( ) 3 and passes through the point 0, 10, not 9, 10 . Choice C is incorrect. This ( ) ( ) equation defines a line that passes through the point 0, 10, not 9, 10 .</p>","correct_answer":["D"],"has_media":false,"has_mathml":false,"has_table":false,"source_created_at":null,"source_updated_at":null,"options":[{"label":"A","content_html":"<p>y = 13x− 1/3</p>","ord":0},{"label":"B","content_html":"<p>y = 9x+1 0</p>","ord":1},{"label":"C","content_html":"<p>y = − x/3 +10</p>","ord":2},{"label":"D","content_html":"<p>y = − x/3 +13</p>","ord":3}],"attribution":{"source_id":"cb_practice_pdf","source_name":"College Board full-length SAT practice tests (PDF)","rights_holder":"College Board","canonical_url":"https://satsuite.collegeboard.org/practice/practice-tests/paper","retrieved_from":"https://satsuite.collegeboard.org/practice/practice-tests/paper","attribution":"Full-length SAT practice tests 4–11 © College Board, published free at satsuite.collegeboard.org.","disclaimer":"Extracted from PDF layout: equations, figures and tables do not survive intact. Use the original PDFs for anything the text renders poorly. SAT® is a trademark registered by the College Board, which is not affiliated with and does not endorse this project.","license":"College Board copyright. Free to download; not licensed for redistribution.","redistributable":false,"item_count":905}}