{"id":"cb_question_bank:fe5242a3-0c7e-4577-ac67-e70e090dfeb8","source_id":"cb_question_bank","source_item_id":"fe5242a3-0c7e-4577-ac67-e70e090dfeb8","external_id":null,"ibn":"08449-DC","question_id":"a8e6bd75","program":"SAT","module":"math","domain_code":"H","domain":"Algebra","skill_code":"H.B.","skill":"Linear functions","difficulty":"E","score_band":2,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"Which of the following is the graph of the equation y, equals 2 x minus 5 in the xy -plane?","stimulus":"","stimulus_html":null,"stem_html":"<p class=\"stem_paragraph \">Which of the following is the graph of the equation <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/c1f03d6b2a3b31240ea41a44201d94b17265b76062ae9e513f788a419023581d\" alt=\"y, equals 2 x minus 5\"></span>&nbsp;in the <span class=\"italic\"><span class=\"italic \">xy</span></span>-plane?</p>\n","rationale_html":"<p>Choice D is correct. In the <span class=\"italic\">xy</span>-plane, the graph of the equation <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/39dda01984e771026b6a8a741d3ebb66f1a29f1e81583b67f8d50f6e2dbb783e\" alt=\"y equals, m x plus b\"></span>, where <span class=\"italic\">m</span> and <span class=\"italic\">b</span> are constants, is a line with slope <span class=\"italic\">m</span> and <span class=\"italic\">y</span>-intercept <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/9dd934c7a6127135240926c5f7629e6538b169f04d5b05cda606fb0a36f0fb9c\" alt=\"with coordinates 0 comma b\"></span>. Therefore, the graph of <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/c1f03d6b2a3b31240ea41a44201d94b17265b76062ae9e513f788a419023581d\" alt=\"y equals, 2 x minus 5\"></span> in the <span class=\"italic\">xy</span>-plane is a line with slope 2 and a <span class=\"italic\">y</span>-intercept <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/8970bb09a4251fb32cef28dd21d8899a7947601077cb1c97a34640affd64dd3f\" alt=\"with coordinates 0 comma negative 5\"></span>. Having a slope of 2 means that for each increase in <span class=\"italic\">x</span> by 1, the value of <span class=\"italic\">y</span> increases by 2. Only the graph in choice D has a slope of 2 and crosses the <span class=\"italic\">y</span>-axis at <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/8970bb09a4251fb32cef28dd21d8899a7947601077cb1c97a34640affd64dd3f\" alt=\"the point with coordinates 0 comma negative 5\"></span>. Therefore, the graph shown in choice D must be the correct answer.</p><p>Choices A, B, and C are incorrect. The graph of <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/c1f03d6b2a3b31240ea41a44201d94b17265b76062ae9e513f788a419023581d\" alt=\"y equals, 2 x minus 5\"></span> in the <span class=\"italic\">xy</span>-plane is a line with slope 2 and a <span class=\"italic\">y</span>-intercept at <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/8970bb09a4251fb32cef28dd21d8899a7947601077cb1c97a34640affd64dd3f\" alt=\"the point with coordinates 0 comma negative 5\"></span>. The graph in choice A crosses the <span class=\"italic\">y</span>-axis at the point <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/4296c1030d1f0df71b1287dd4a29304531933ca74e1d8c6d45b3c22c2381638b\" alt=\"with coordinates 0 comma 2 point 5\"></span>, not <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/8970bb09a4251fb32cef28dd21d8899a7947601077cb1c97a34640affd64dd3f\" alt=\"the point with coordinates 0 comma negative 5\"></span>, and it has a slope of <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/acd304db4db3ee4a427462753769f86b9941b320104a3856da731c39db5d894c\" alt=\"one-half\"></span>, not 2. The graph in choice B crosses the <span class=\"italic\">y</span>-axis at <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/8970bb09a4251fb32cef28dd21d8899a7947601077cb1c97a34640affd64dd3f\" alt=\"the point with coordinates 0 comma negative 5\"></span>; however, the slope of this line is <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/a546b5be2c97283e2d1e93605f422844d5a87f3418a61a7d23019eb596b64f17\" alt=\"negative 2\"></span>, not 2. The graph in choice C has a slope of 2; however, the graph crosses the <span class=\"italic\">y</span>-axis at <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/935b566455aff79bebf91aedcce3799bce6d3a09b4646361031e7efd2749f732\" alt=\"the point with coordinates 0 comma 5\"></span>, not <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/8970bb09a4251fb32cef28dd21d8899a7947601077cb1c97a34640affd64dd3f\" alt=\"the point with coordinates 0 comma negative 5\"></span>.</p><p>&nbsp;</p><p></p>\n","correct_answer":["D"],"has_media":true,"has_mathml":false,"has_table":false,"source_created_at":"2023-08-02T20:25:59.636000+00:00","source_updated_at":"2023-08-02T20:25:59.636000+00:00","options":[{"label":"A","content_html":"<p class=\"choice_paragraph \">&nbsp;</p><p><img src=\"/api/assets/719e1d427dedc0dedbe6975c11896b119068f5cd7ecd7f24a38c86a2d21546bd\" alt=\"The figure presents the graph of a line in the x y-plane with the origin labeled O. The numbers negative five through five are indicated on each axis. The line begins in quadrant 3 and moves upward and to the right. It crosses the x-axis at negative 5 and the y-axis at 2 point 5, ending in quadrant 1\" width=\"124\" height=\"131\"></p><p>&nbsp;</p><p></p>\n","ord":0},{"label":"B","content_html":"<p class=\"choice_paragraph \">&nbsp;</p><p><img src=\"/api/assets/5f25b0bde920f061b4c2dcd65672acb2b00f2d6d886ce4795cfe3832c09dc78c\" alt=\"The figure presents the graph of a line in the x y-plane with the origin labeled O. The numbers negative five through five are indicated on each axis. The line begins in quadrant 2 and moves downward and to the right. It crosses the x-axis at negative 2 point 5 and the y-axis at negative 5, ending in quadrant 4\" width=\"124\" height=\"131\"></p><p>&nbsp;</p><p></p>\n","ord":1},{"label":"C","content_html":"<p class=\"choice_paragraph \">&nbsp;</p><p><img src=\"/api/assets/13153a88123df4123ee324e01e7995dee7df93a80a6abe64e958641a224fa0c8\" alt=\"The figure presents the graph of a line in the x y-plane with the origin labeled O. The numbers negative five through five are indicated on each axis. The line begins in quadrant 3 and moves upward and to the right. It crosses the x-axis at negative 2 point 5 and the y-axis at 5, ending in quadrant 1\" width=\"124\" height=\"131\"></p><p>&nbsp;</p><p></p>\n","ord":2},{"label":"D","content_html":"<p class=\"choice_paragraph \">&nbsp;</p><p><img src=\"/api/assets/f47f3b709dcc99724119482a1727383e2579453d6e948df43cfb57d6496155d4\" alt=\"The figure presents the graph of a line in the x y-plane with the origin labeled O. The numbers negative five through five are indicated on each axis. The line begins in quadrant 3 and moves upward and to the right. It crosses the y-axis at negative 5 and the x-axis at 2 point 5, ending in quadrant 1\" width=\"124\" height=\"131\"></p><p>&nbsp;</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}}