{"id":"cb_question_bank:9b342030-19c4-47e3-b3ad-424fa194f6df","source_id":"cb_question_bank","source_item_id":"9b342030-19c4-47e3-b3ad-424fa194f6df","external_id":null,"ibn":"028832-DC","question_id":"ab7740a8","program":"SAT","module":"math","domain_code":"Q","domain":"Problem-Solving and Data Analysis","skill_code":"Q.D.","skill":"Two-variable data: Models and scatterplots","difficulty":"M","score_band":5,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"In which of the following tables is the relationship between the values of x and their corresponding y -values nonlinear?","stimulus":"","stimulus_html":null,"stem_html":"<p class=\"stem_paragraph \">In which of the following tables is the relationship between the values of <span class=\"italic\">x</span> and their corresponding <span class=\"italic \">y</span>-values nonlinear?</p>\n","rationale_html":"<p>Choice D is correct. The relationship between the values of <span class=\"italic\">x</span> and their corresponding <span class=\"italic\">y</span>-values is nonlinear if the rate of change between these pairs of values isn’t constant. The table for choice D gives four pairs of values: <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/0f2f263e4a8edeb988458eef6c077234062384b10c8ef99ba772f80b38c08f25\" alt=\"the point with coordinates 1 comma 6 \"></span>,<span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/18c6684c00ea714142320941a76e1c553d7a54552fd0a1f18090c79845157e4a\" alt=\"the point with coordinates 2 comma 12\"></span>, <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/ef7168dbba705d5cac0c7f62cd7b2d41f6f283bc4a33184f6075c6cd81a86e89\" alt=\"the point with coordinates 3 comma 24 \"></span>, and <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/5c88d725a05cd8c59b0f8387976242df385c0d7dcdf3eb1febea79ce9b3645b1\" alt=\"the point with coordinates 4 comma 48 \"></span>. Finding the rate of change, or slope, between <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/0f2f263e4a8edeb988458eef6c077234062384b10c8ef99ba772f80b38c08f25\" alt=\"the point with coordinates 1 comma 6 \"></span> and <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/18c6684c00ea714142320941a76e1c553d7a54552fd0a1f18090c79845157e4a\" alt=\"the point with coordinates 2 comma 12\"></span> by using the slope formula, <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/a03975b16d4ea2c3b86d4b581b9e016521425404cedaa5512efb6e3d64a3280f\" alt=\"the fraction with numerator y sub 2 minus y sub 1, and denominator x sub 2 minus x sub 1, end fraction\"></span>, yields <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/92870cb90710108e9c51dd6dce4ca487cc578ffa0b7acc4ada11e5ac157a6791\" alt=\"the fraction with numerator 12 minus 6, and denominator 2 minus 1, end fraction\"></span>, or 6. Finding the rate of change between <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/18c6684c00ea714142320941a76e1c553d7a54552fd0a1f18090c79845157e4a\" alt=\"the point with coordinates 2 comma 12\"></span> and <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/ef7168dbba705d5cac0c7f62cd7b2d41f6f283bc4a33184f6075c6cd81a86e89\" alt=\"the point with coordinates 3 comma 24 \"></span> yields <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/3f0f89d1f032b0b1d739b8b0e4c61afa1b0a80c3b189670a92709b88aae21197\" alt=\"the fraction with numerator 24 minus 12, and denominator 3 minus 2, end fraction\"></span>, or 12. Finding the rate of change between <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/ef7168dbba705d5cac0c7f62cd7b2d41f6f283bc4a33184f6075c6cd81a86e89\" alt=\"the point with coordinates 3 comma 24 \"></span> and <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/5c88d725a05cd8c59b0f8387976242df385c0d7dcdf3eb1febea79ce9b3645b1\" alt=\"the point with coordinates 4 comma 48 \"></span> yields <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/67e3ac3f1696efa3d6ef7e6b1a5684472414aaab4e047c68257aec5c14468853\" alt=\"the fraction with numerator 48 minus 24, and denominator 4 minus 3, end fraction\"></span>, or 24. Since the rate of change isn’t constant for these pairs of values, this table shows a nonlinear relationship.</p><p>Choices A, B, and C are incorrect. The rate of change between the values of <span class=\"italic\">x</span> and their corresponding <span class=\"italic\">y</span>-values in each of these tables is constant, being 3, 4, and 5, respectively. Therefore, each of these tables shows a linear relationship.</p><p></p>\n","correct_answer":["D"],"has_media":true,"has_mathml":false,"has_table":false,"source_created_at":"2023-08-02T20:25:59.622000+00:00","source_updated_at":"2023-08-02T20:25:59.622000+00:00","options":[{"label":"A","content_html":"<p class=\"choice_paragraph \">\n            <span class=\"inline_image \">\n            </span>\n          </p><p>\n          <img src=\"/api/assets/1f6460312e5503af0919f94f281edc7ae8e44d63f008e82b096ef0dfb3e152ce\" alt=\"The answer choice presents a 2 row table, with 4 columns of data. The heading for row 1 is “x,” and the heading for row 2 is “y.” The data in the table are as follows. Column 1. x is 1. y is 8. Column 2. x is 2. y is 11. Column 3. x is 3. y is 14. Column 4. x is 4. y is 17.\" width=\"122\" height=\"34\"></p><p></p>\n","ord":0},{"label":"B","content_html":"<p class=\"choice_paragraph \">\n            <span class=\"inline_image \">\n            </span>\n          </p><p>\n          <img src=\"/api/assets/da8e6c823e574458488d0b81b883f19b0eae88ab958adcbb2fd28cffa5ed639e\" alt=\"The answer choice presents a 2 row table, with 4 columns of data. The heading for row 1 is “x,” and the heading for row 2 is “y.” The data in the table are as follows. Column 1. x is 1. y is 4. Column 2. x is 2. y is 8. Column 3. x is 3. y is 12. Column 4. x is 4. y is 16.\" width=\"122\" height=\"34\"></p><p></p>\n","ord":1},{"label":"C","content_html":"<p class=\"choice_paragraph \">\n            <span class=\"inline_image \">\n            </span>\n          </p><p>\n          <img src=\"/api/assets/5d8b22e459b92d77747ec828a781f776e48046f8ec8910c58451a8003573983a\" alt=\"The answer choice presents a 2 row table, with 4 columns of data. The heading for row 1 is “x,” and the heading for row 2 is “y.” The data in the table are as follows. Column 1. x is 1. y is 8. Column 2. x is 2. y is 13. Column 3. x is 3. y is 18. Column 4. x is 4. y is 23.\" width=\"122\" height=\"34\"></p><p></p>\n","ord":2},{"label":"D","content_html":"<p class=\"choice_paragraph \">\n            <span class=\"inline_image \">\n            </span>\n          </p><p>\n          <img src=\"/api/assets/3225def2914aada3e3a75cf2de1741f07d67b7d0812246c8409d1ab276fcaa55\" alt=\"The answer choice presents a 2 row table, with 4 columns of data. The heading for row 1 is “x,” and the heading for row 2 is “y.” The data in the table are as follows. Column 1. x is 1. y is 6. Column 2. x is 2. y is 12. Column 3. x is 3. y is 24. Column 4. x is 4. y is 48.\" width=\"122\" height=\"34\"></p><p></p>\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}}