{"id":"cb_question_bank:f85a29b8-7af3-4d3c-9139-4bb0056c20d5","source_id":"cb_question_bank","source_item_id":"f85a29b8-7af3-4d3c-9139-4bb0056c20d5","external_id":null,"ibn":"09915-DC","question_id":"8a1544f1","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":"What is the equation of the line shown in the xy -plane above?","stimulus":"The figure presents a graph of a line in the x y-plane with the origin labeled O. The numbers negative five through positive five are indicated along the x- and y-axes. The line begins in the second quadrant and moves downward and to the right. It crosses the y-axis at 3 and the x-axis at one.","stimulus_html":"<div class=\"stimulus_reference \">\n        <div class=\"standalone_image \">\n          <img src=\"/api/assets/ac35376a50e36ef186e1c81f5908e543dcc305372470fbf17892739d13d07520\" alt=\"The figure presents a graph of a line in the x y-plane with the origin labeled O. The numbers negative five through positive five are indicated along the x- and y-axes.  The line begins in the second quadrant and moves downward and to the right. It crosses the y-axis at 3 and the x-axis at one.\" width=\"172\" height=\"178\"></div>\n      </div>\n","stem_html":"<p class=\"stem_paragraph \">What is the equation of the line shown in the <span class=\"italic\">xy</span>-plane above?</p>\n","rationale_html":"<p>Choice B is correct. Any line in the <span class=\"italic\">xy</span>-plane can be defined by an equation in the form <span class=\"italic\">y</span> = <span class=\"italic\">mx</span> + <span class=\"italic\">b</span>, where <span class=\"italic\">m</span> is the slope of the line and <span class=\"italic\">b</span> is the <span class=\"italic\">y</span>-coordinate of the <span class=\"italic\">y</span>-intercept of the line. From the graph, the <span class=\"italic\">y</span>-intercept of the line is (0, 3). Therefore, <span class=\"italic\">b</span> = 3. The slope of the line is the change in the value of <span class=\"italic\">y</span> divided by the change in the value of<span class=\"italic\"> x</span> for any two points on the line. The line shown passes through (0, 3) and (1, 0), so <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/09db13e56c2d8ee2d39daa46d5d08c873edf91269af9b2303dbf61a93c530ff7\" alt=\"m equals, the fraction with numerator 3 minus zero, and denominator zero minus 1\"></span>, or <span class=\"italic\">m</span> = –3. Therefore, the equation of the line is <span class=\"italic\">y</span> = –3<span class=\"italic\">x</span> + 3.</p><p>Choices A and C are incorrect because the equations given in these choices represent a line with a positive slope. However, the line shown has a negative slope. Choice D is incorrect because the equation given in this choice represents a line with slope of <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/df9326954ce9067896fc6376d068ad8023f68d3be50df9afe4ec1a773cf48f9a\" alt=\"negative one third\"></span>. However, the line shown has a slope of&nbsp; –3.</p><p></p>\n","correct_answer":["B"],"has_media":true,"has_mathml":false,"has_table":false,"source_created_at":"2023-08-02T20:25:59.637000+00:00","source_updated_at":"2023-08-02T20:25:59.637000+00:00","options":[{"label":"A","content_html":"<span class=\"math_expression \">\n            <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/6470dae3135d0f3ffabbc2847eea8e9073473526791dbf786cdf098af70a30f0\" alt=\"y equals 3 x minus 3\"></span></span>\n","ord":0},{"label":"B","content_html":"<span class=\"math_expression \">\n            <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/845348a32f60d9fc796a251ba2d6d897abe80be0d9fe9ad50e14b9b6211e5e14\" alt=\"y equals negative 3 x plus 3\"></span></span>\n","ord":1},{"label":"C","content_html":"<span class=\"math_expression \">\n            <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/d3fbdf21080c7980236553270b564516c40ae1511d8da95ff827f07d392ff775\" alt=\"y equals one-third x minus 3\"></span></span>\n","ord":2},{"label":"D","content_html":"<span class=\"math_expression \">\n            <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/f9d2822ff6be77755e1c960be5e6697bf5c05c255f2a80879de33da38e774020\" alt=\"y equals negative one-third x plus 3\"></span></span>\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}}