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Unformatted text preview: Lecture 9: Coordinates on the plane, distance formula, equations and their graphs June 14, 2010 I once asked a class of undergraduates why the graph of a linear equation is a line. One student looked at me, kind of tilted her head, and said, Well, duh! Why do you think its called linear? Well, it was a trick question. The graph of a linear equation is not always a line. I can show you. Here (in red) is a portion of the graph of r = 3 4 - 5 2 : Minus 10 Minus 5 5 10 Of course, r and are polar coordinates, but I mean to make a point. The reason that the graph of a linear equation is a line must have something to do with the special nature of the cartesian coordinate system , because in other coordinate systems, this is not true. So, the real question is, What is it about the cartesian coordinate system that assures that the graph of a linear equation is a straight line? STANDARD COORDINATE SYSTEM IN A PLANE Pr esent e ` a la mani` ere dIrma Rombauer, auteure de The Joy of Cooking . Take: 1 unmarked plane 1 unit of length In the plane, select: 2 lines that are perpendicular to one another a direction on each of the lines Using the unit of length, the point where the lines cross as the origin and the selected directions create a coordinate system on each of the lines following the recipe for Coordinate System on a Line (in previous lecture). Call one of the lines the x-axis and call the other the y-axis, and call the coordinate functions on them x and y respectively. Now extend therespectively....
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