{"id":"cb_question_bank:08ae0f01-75f8-491a-9958-ba37830d42e1","source_id":"cb_question_bank","source_item_id":"08ae0f01-75f8-491a-9958-ba37830d42e1","external_id":"77e2c729-a66a-47de-9258-130399ad202e","ibn":null,"question_id":"548a4929","program":"SAT","module":"math","domain_code":"H","domain":"Algebra","skill_code":"H.B.","skill":"Linear functions","difficulty":"M","score_band":5,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"The function h is defined by h left parenthesis x right parenthesis equals 4 x plus 28 . The graph of y equals h left parenthesis x right parenthesis in the xy -plane has an x -intercept at left parenthesis a comma 0 right parenthesis and a y -intercept at left parenthesis 0 comma b right parenthesis , where a and b are constants. What is the value of a plus b ?","stimulus":"","stimulus_html":null,"stem_html":"

The function h\n is defined by hx=4x+28. The graph of y=hx in the xy-plane has an x-intercept at a,0 and a y-intercept at 0,b, where a\n and b\n are constants. What is the value of \n\ta\n\t+\n\tb\n\n?

","rationale_html":"

Choice A is correct. The x-intercept of a graph in the xy-plane is the point on the graph where \n\ty\n\t=\n\t0\n\n. It's given that function h\n is defined by hx=4x+28. Therefore, the equation representing the graph of y=hx is \n\ty\n\t=\n\t\n\t\t\n\t\t\t4\n\t\t\tx\n\t\t\n\t\t+\n\t\t28\n\t\n\n. Substituting 0\n for y\n in the equation \n\ty\n\t=\n\t\n\t\t\n\t\t\t4\n\t\t\tx\n\t\t\n\t\t+\n\t\t28\n\t\n\n yields \n\t0\n\t=\n\t\n\t\t\n\t\t\t4\n\t\t\tx\n\t\t\n\t\t+\n\t\t28\n\t\n\n. Subtracting 28\n from both sides of this equation yields \n\t-28\n\t=\n\t\n\t\t4\n\t\tx\n\t\n\n. Dividing both sides of this equation by 4\n yields \n\t-7\n\t=\n\tx\n\n. Therefore, the x-intercept of the graph of y=hx in the xy-plane is -7,0. It's given that the x-intercept of the graph of y=hx is a,0. Therefore, \n\ta\n\t=\n\t-7\n\n. The y-intercept of a graph in the xy-plane is the point on the graph where \n\tx\n\t=\n\t0\n\n. Substituting 0\n for x\n in the equation \n\ty\n\t=\n\t\n\t\t\n\t\t\t4\n\t\t\tx\n\t\t\n\t\t+\n\t\t28\n\t\n\n yields y=40+28, or \n\ty\n\t=\n\t28\n\n. Therefore, the y-intercept of the graph of y=hx in the xy-plane is 0,28. It's given that the y-intercept of the graph of y=hx is 0,b. Therefore, \n\tb\n\t=\n\t28\n\n. If \n\ta\n\t=\n\t-7\n\n and \n\tb\n\t=\n\t28\n\n, then the value of \n\ta\n\t+\n\tb\n\n is -7+28, or 21\n.

\n

Choice B is incorrect. This is the value of b\n, not \n\ta\n\t+\n\tb\n\n.

\n

Choice C is incorrect and may result from conceptual or calculation errors.

\n

Choice D is incorrect. This is the value of \n\t\n\t\t-\n\t\ta\n\t\n\t+\n\tb\n\n, not \n\ta\n\t+\n\tb\n\n.

","correct_answer":["A"],"has_media":false,"has_mathml":true,"has_table":false,"source_created_at":"2023-08-02T20:25:59.811000+00:00","source_updated_at":"2023-08-02T20:25:59.811000+00:00","options":[{"label":"A","content_html":"

21\n

","ord":0},{"label":"B","content_html":"

28\n

","ord":1},{"label":"C","content_html":"

32\n

","ord":2},{"label":"D","content_html":"

35\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}}