{"id":"cb_question_bank:eddb15a2-2fa1-4046-af16-79ad436e1844","source_id":"cb_question_bank","source_item_id":"eddb15a2-2fa1-4046-af16-79ad436e1844","external_id":null,"ibn":"027788-DC","question_id":"8a6de407","program":"SAT","module":"math","domain_code":"H","domain":"Algebra","skill_code":"H.B.","skill":"Linear functions","difficulty":"M","score_band":4,"answer_type":"spr","answer_source":"rationale","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"The function f is defined by f of x equals, m x plus b , where m and b are constants. If f of 0 equals 18 and f of 1 equals 20 , what is the value of m ?","stimulus":"","stimulus_html":null,"stem_html":"<p class=\"stem_paragraph \">The function <span class=\"italic\">f</span> is defined by <span class=\"math_expression \"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/85d346e80696592103a24156028b524124e60208306aaa1d2b81366c09e2f8e4\" alt=\"f of x equals, m x plus b\"></span></span>, where <span class=\"italic\">m</span> and <span class=\"italic\">b</span> are constants. If <span class=\"math_expression \"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/65798693a9476865606a6fc2a17005141b3b0e8ff1636cf1aed7fdb20709277b\" alt=\"f of 0 equals 18 \"></span></span> and <span class=\"math_expression \"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/c7294d403548311db5c38f1aa0d814697a13e2dfffa06a1c3d92795e9f466c5c\" alt=\"f of 1 equals 20\"></span></span>, what is the value of <span class=\"italic\">m</span>&nbsp;?</p>\n","rationale_html":"<p>The correct answer is 2. The slope-intercept form of an equation for a line is <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> is the slope and <span class=\"italic\">b</span> is the <span class=\"italic\">y</span>-coordinate of the <span class=\"italic\">y</span>-intercept. Two ordered pairs, <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/b0f2bfb2bfb5f9eade6a69ea162cb4065ad6966d97ea9cf386ec63744405b3ed\" alt=\"x sub 1 comma y sub 1 \"></span> and <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/091f2398b4b15d3ea165d86a402c73fc2155faaa6492970e80df4ed77ba19888\" alt=\"x sub 2 comma y sub 2\"></span>, can be used to compute the slope using the formula <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/d90665e9527746054088c372f023f7eaa687ac5da59918408884c2d405e79dcc\" alt=\"m equals, the fraction with numerator y sub 2, minus y sub 1, and denominator x sub 2, minus x sub 1, end fraction\"></span>. It’s given that <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/65798693a9476865606a6fc2a17005141b3b0e8ff1636cf1aed7fdb20709277b\" alt=\"f of 0 equals 18 \"></span> and <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/c7294d403548311db5c38f1aa0d814697a13e2dfffa06a1c3d92795e9f466c5c\" alt=\"f of 1 equals 20 \"></span>; therefore, the two ordered pairs for this line are <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/8fe58bacc748369c1246ac1ff75aa93598b7a94811b579cf74705db33c903466\" alt=\"0 comma 18 \"></span> and <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/cd6aaf157fd378822eb459ecee30bebcd9a732d1645e856b36514dba280dfa8f\" alt=\"1 comma 20\"></span>. Substituting these values for <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/b0f2bfb2bfb5f9eade6a69ea162cb4065ad6966d97ea9cf386ec63744405b3ed\" alt=\"x sub 1 comma y sub 1\"></span> and <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/091f2398b4b15d3ea165d86a402c73fc2155faaa6492970e80df4ed77ba19888\" alt=\"x sub 2 comma y sub 2 \"></span> gives <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/c28c333e66cf8d08f733b116fd24f8bd007b9e5171162e788bbaf8095eb58167\" alt=\"the fraction with numerator 20 minus 18, and denominator 1 minus 0, end fraction, equals, the fraction 2 over 1\"></span>, or 2.</p>\n","correct_answer":["2"],"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":[],"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}}