{"id":"cb_question_bank:90aca617-77d8-45b7-bcb5-252e4073a3fa","source_id":"cb_question_bank","source_item_id":"90aca617-77d8-45b7-bcb5-252e4073a3fa","external_id":null,"ibn":"031698-DC","question_id":"30281058","program":"SAT","module":"math","domain_code":"P","domain":"Advanced Math","skill_code":"P.B.","skill":"Nonlinear equations in one variable and systems of equations in two variables","difficulty":"H","score_band":6,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"In the xy -plane, the graph of y equals, x squared minus 9 intersects line p at the point with coordinates 1 comma a and the point with coordinates 5 comma b , where a and b are constants. What is the slope of line p ?","stimulus":"","stimulus_html":null,"stem_html":"<p class=\"stem_paragraph \">In the <span class=\"italic \">xy</span>-plane, the graph of <span class=\"math_expression \"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/0c50656d5694d0b12c1346237f286d21488187bfd339f798902f3875d2f45e84\" alt=\"y equals, x squared minus 9 \"></span></span> intersects line&nbsp;<span class=\"italic\">p</span> at <span class=\"math_expression \"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/846983729af323711391b81d13ceb6a834b44a716ec7b17da49fb2b6eb220eba\" alt=\"the point with coordinates 1 comma a\"></span></span> and <span class=\"math_expression \"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/0f877a6684ac49f818b29286d06a0f5d22f1af8da9084040ce6300c590113cb9\" alt=\"the point with coordinates 5 comma b\"></span></span>, where <span class=\"italic\">a</span> and <span class=\"italic\">b</span> are constants. What is the slope of line&nbsp;<span class=\"italic\">p </span>?</p>\n","rationale_html":"<p>Choice A is correct. It’s given that the graph of <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/0c50656d5694d0b12c1346237f286d21488187bfd339f798902f3875d2f45e84\" alt=\"y equals, x squared, minus 9 \"></span> and line <span class=\"italic\">p</span> intersect at <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/846983729af323711391b81d13ceb6a834b44a716ec7b17da49fb2b6eb220eba\" alt=\"the point with coordinates 1 comma a\"></span> and <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/0f877a6684ac49f818b29286d06a0f5d22f1af8da9084040ce6300c590113cb9\" alt=\"the point with coordinates 5 comma b\"></span>. Therefore, the value of <span class=\"italic\">y</span> when <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/6e4319fe2c5755fc5aa3f69e1a43b989d061cbb17c450f24b51a6616f131de4b\" alt=\"x equals 1 \"></span> is the value of <span class=\"italic\">a</span>, and the value of <span class=\"italic\">y</span> when <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/24796268b6fb782d78745c6cfef1c4479da9853b4b07eafd4bc226fb068e3bc1\" alt=\"x equals 5  \"></span> is the value of <span class=\"italic\">b</span>. Substituting 1 for <span class=\"italic\">x</span> in the given equation yields <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/1674af65fa713acee7ff79de9efea505c40fd6c565ed2e3e74518e75e8371b3d\" alt=\"y equals, 1 squared minus 9\"></span>, or <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/875fbe4027a52de147ea3be5be87674d7cfe8dc28867101272a492180dad75ec\" alt=\"y equals negative 8\"></span>. Similarly, substituting 5 for <span class=\"italic\">x</span> in the given equation yields <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/9972789ace025110c1e63476a1da45d2d40f607141a9f22636705b4d5c78aa86\" alt=\"y equals, 5 squared minus 9\"></span>, or <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/e377da87224983f2bae63f3e01073b992f20f515fce2561d457d6705a84d8d9b\" alt=\"y equals 16\"></span>. Therefore, the intersection points are <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/b4e5ae4d1c3cfd71b1c638351c8c1bd7884bb80417d56e7f65291520f7e71c3d\" alt=\"the point with coordinates 1 comma negative 8 \"></span> and <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/8cb2d46cd93548980a9c4294b04c96c6638f297f7bd6aa376c9cb1858af015b0\" alt=\"the point with coordinates 5 comma 16\"></span>. The slope of line <span class=\"italic\">p</span> is the ratio of the change in <span class=\"italic\">y</span> to the change in <span class=\"italic\">x</span> between these two points: <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/8c9e8ebb9b7631f930d2a309165d2779e9d25c3523edfb20c30c260a13021d9d\" alt=\"the fraction with numerator 16 minus negative 8, and denominator 5 minus 1, end fraction, equals the fraction 24 over 4\"></span>, or 6.</p><p>Choices B, C, and D are incorrect and may result from conceptual or calculation errors in determining the values of <span class=\"italic\">a</span>, <span class=\"italic\">b</span>, or the slope of line <span class=\"italic\">p</span>.</p><p></p>\n","correct_answer":["A"],"has_media":true,"has_mathml":false,"has_table":false,"source_created_at":"2023-08-02T20:25:59.627000+00:00","source_updated_at":"2023-08-02T20:25:59.627000+00:00","options":[{"label":"A","content_html":"<span class=\"choice_cell align:center \">\n            <span class=\"math_expression \">\n              <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/639893cf6218e7761ea1a899333fd0db752650fb0f7ac5e0f3ed798d6c494deb\" alt=\"6\"></span></span>\n          </span>\n","ord":0},{"label":"B","content_html":"<span class=\"choice_cell align:center \">\n            <span class=\"math_expression \">\n              <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/8ed3fca031fe20f2c313bfecec888594f5ca2d81fb2d396d54689fb48e3ee8df\" alt=\"2\"></span></span>\n          </span>\n","ord":1},{"label":"C","content_html":"<span class=\"choice_cell align:center \">\n            <span class=\"math_expression \">\n              <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/ce74cbabbaf45617e6561aad72315be422e849fe95e17b32d71443c7ee5c57e7\" alt=\"negative 2\"></span></span>\n          </span>\n","ord":2},{"label":"D","content_html":"<span class=\"choice_cell align:center \">\n            <span class=\"math_expression \">\n              <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/f8ac4e862b233acbee95c501658ff49dd21661d2a931c76a597fe7d20c5d70df\" alt=\"negative 6\"></span></span>\n          </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}}