\r\n" );
document.write( "No, there is nothing special about 1 and 3, except that they are \r\n" );
document.write( "easy numbers to work with. But you are free to choose ANY value \r\n" );
document.write( "for an x-coordinate to find the corresponding y-coordinate. You \r\n" );
document.write( "are also free to choose ANY value for a y-coordinate to find the \r\n" );
document.write( "corresponding x-coordinate. However, if you choose very large \r\n" );
document.write( "numbers, you will have to make a very large graph, and if you \r\n" );
document.write( "choose values hard to work with, like fractions and decimals, \r\n" );
document.write( "the work will be harder. But theoretically you can choose any \r\n" );
document.write( "numbers that you want to.\r\n" );
document.write( "\r\n" );
document.write( "Every time you choose a number at random for one variable's \r\n" );
document.write( "coordinate, and substitute to find the other variable's \r\n" );
document.write( "coordinate, you have found another point on the SAME line.\r\n" );
document.write( "\r\n" );
document.write( "Suppose we arbitrarily choose y = 4. Then we substitute 4 for y in\r\n" );
document.write( "\r\n" );
document.write( "y + x = -3\r\n" );
document.write( "4 + x = -3\r\n" );
document.write( " x = -7\r\n" );
document.write( "\r\n" );
document.write( "That gives us the point (x,y) = (-7,4), and we can plot it like this:\r\n" );
document.write( "\r\n" );
document.write( "
\r\n" );
document.write( "\r\n" );
document.write( "--\r\n" );
document.write( "\r\n" );
document.write( "Now suppose we arbitrarily choose x = 5. Then we substitute 5 for x in\r\n" );
document.write( "\r\n" );
document.write( "y + x = -3\r\n" );
document.write( "y + 5 = -3\r\n" );
document.write( " y = -8\r\n" );
document.write( "\r\n" );
document.write( "That gives us the point (x,y) = (5,-8), and we can plot it like this:\r\n" );
document.write( "\r\n" );
document.write( "
\r\n" );
document.write( "\r\n" );
document.write( "--\r\n" );
document.write( "\r\n" );
document.write( "Now suppose we arbitrarily choose y = -7. Then we substitute -7 for y in\r\n" );
document.write( "\r\n" );
document.write( " y + x = -3\r\n" );
document.write( "-7 + x = -3\r\n" );
document.write( " x = 4\r\n" );
document.write( "\r\n" );
document.write( "That gives us the point (x,y) = (4,-7), and we can plot it like this:\r\n" );
document.write( "\r\n" );
document.write( "
\r\n" );
document.write( "\r\n" );
document.write( "Now suppose we arbitrarily choose x = -2. Then we substitute -2 for x in\r\n" );
document.write( "\r\n" );
document.write( " y + x = -3\r\n" );
document.write( " y + (-2) = -3\r\n" );
document.write( " y - 2 = -3\r\n" );
document.write( " y = -1\r\n" );
document.write( " \r\n" );
document.write( "That gives us the point (x,y) = (-2,-1), and we can plot it like this:\r\n" );
document.write( "\r\n" );
document.write( "
\r\n" );
document.write( "\r\n" );
document.write( "Now suppose we arbitrarily choose y = 2. Then we substitute 2 for y in\r\n" );
document.write( "\r\n" );
document.write( " y + x = -3\r\n" );
document.write( " 2 + x = -3\r\n" );
document.write( " x = -5\r\n" );
document.write( " \r\n" );
document.write( " \r\n" );
document.write( "That gives us the point (x,y) = (-5,2), and we can plot it like this:\r\n" );
document.write( "\r\n" );
document.write( "
\r\n" );
document.write( "\r\n" );
document.write( "Now we lay a ruler along those points and we will\r\n" );
document.write( "find they will all lie on a straight line, like\r\n" );
document.write( "this green line below:\r\n" );
document.write( "\r\n" );
document.write( "
\r\n" );
document.write( "\r\n" );
document.write( "So you see we got the graph of the line without using 1 or 3.\r\n" );
document.write( "But of course you can use 1 and 3 if you like. Notice that you\r\n" );
document.write( "only need two points to draw a line. So you can draw the line\r\n" );
document.write( "just by getting ANY two points on it. However, since people do \r\n" );
document.write( "make mistakes, you should always get at least three points as \r\n" );
document.write( "a check, because if you were to get three points that are not \r\n" );
document.write( "in a straight line, then you would know that at least one of them \r\n" );
document.write( "was wrong. But if you only get two points, you can always draw a\r\n" );
document.write( "line through them, even if you made a mistake on one of them. So\r\n" );
document.write( "if you are going to get just 2 points, be sure not to make a \r\n" );
document.write( "mistake!\r\n" );
document.write( "\r\n" );
document.write( "Edwin
\n" );
document.write( "![\"\"](\"/images/stars/stars-13.gif\")
