Find the equation of the family of curves having the given slope, and the equation of the curve of the family which passes through the given point, in each of the following: (a) m = 4x; (1,5) (b) m = √x; (9, 18) (c) m = (x - 1)³; (3,0)

College Algebra (MindTap Course List)
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Author:R. David Gustafson, Jeff Hughes
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Chapter2: Functions And Graphs
Section2.4: Writing And Graphing Equations Of Lines
Problem 80E
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Find the equation of the family of curves having the given slope, and the equation of the curve of the
family which passes through the given point, in each of the following:
(a) m = 4x; (1,5)
(b) m = √x; (9, 18)
(e) m = x/y: (4,2)
(c) m = (x - 1)³; (3,0)
(f) m = x²y³; (3,2)
(d) m = 1/x²; (1, 2)
(g) m = 2y/x; (2,8)
(h) m = xy/(1+x²); (3,5)
Transcribed Image Text:Find the equation of the family of curves having the given slope, and the equation of the curve of the family which passes through the given point, in each of the following: (a) m = 4x; (1,5) (b) m = √x; (9, 18) (e) m = x/y: (4,2) (c) m = (x - 1)³; (3,0) (f) m = x²y³; (3,2) (d) m = 1/x²; (1, 2) (g) m = 2y/x; (2,8) (h) m = xy/(1+x²); (3,5)
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