08-26-2009-problem

08-26-2009-problem - -b-plane. A line in the m-b-plane is a...

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Problem Introduction. For any choice of numbers for m and b , we get a line in the x - y -plane given by the equation y = m x + b. But a value for m and a value for b also determines a point in the m - b -plane. 1 0 5 5 1 0 1 0 5 5 1 0 1 0 5 5 1 0 1 0 5 5 1 0 Figure 1. The lines y = 2 x +3, y = 5 x -2 and Y = -(1/2) x +1 in the x - y -plane. Figure 2. The points (2,3), (5,2) and (-1/2, 1) in the m - b -plane. We see this way that every point in the m - b -plane determines a line in the x - y -plane and every non-vertical line in the x - y -plane determines a point in the m
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Unformatted text preview: -b-plane. A line in the m-b-plane is a collection of m-b-points. Each such point determines a line in the x-y-plane. So a line in the m-b-plane determines a family of lines in the x-y-plane. Problem 1. Let b = 3 m + 5 be a line in the m-b-plane. What is the corresponding family of lines in the x-y-plane? Problem 2. Every non-vertical line in the m-b-plane has an equation of the form b = S m + T. Describe the corresponding family of lines in the x-y-plane in terms of S and T ....
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This note was uploaded on 11/23/2011 for the course MATH 1551 taught by Professor Malisoff during the Fall '08 term at LSU.

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