document.write( "Question 593787: I have an algebra question. On my worksheet, it says \"Determine a relationship between the x- and y-values. Write an equation.\" I know how to do that, but for the second problem, the ordered pairs are (2,3), (3,5), (4,7), and (5,9). I put them in a table and it looks like the relationship is a sequence, because as you go up, you add 1 to 2 to make 3, and then you add 2 to 3 to make 5, and so on. How would you write this as an equation? (i.e. y=x+3)\r
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Algebra.Com's Answer #376455 by AnlytcPhil(1806)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "x 2 3 4 5\r\n" );
document.write( "y 3 5 7 9\r\n" );
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document.write( "There are more than one way to do this kind of problem.\r\n" );
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document.write( "First way:\r\n" );
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document.write( "Look at (2,3).  If you add 1 to 3 you get 4, and 4 is twice 2.\r\n" );
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document.write( "Look at (3,5).  If you add 1 to 5 you get 6, and 6 is twice 3.\r\n" );
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document.write( "Look at (4,7).  If you add 1 to 7 you get 8, and 8 is twice 4.\r\n" );
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document.write( "Look at (5,9).  If you add 1 to 9 you get 10, and 10 is twice 5.\r\n" );
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document.write( "Now take the general case (x,y) and say the same thing about it:\r\n" );
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document.write( "Look at (x,y).  If you add 1 to y you get y+1, and y+1 is twice x.\r\n" );
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document.write( "Write that as an equation:\r\n" );
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document.write( "             y+1 = 2x\r\n" );
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document.write( "which simplifies to\r\n" );
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document.write( "               y = 2x - 1\r\n" );
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document.write( "Second way:\r\n" );
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document.write( "Look at the point (2,3).  If you double 2 you get 4, and 4 is 1 more than 3.\r\n" );
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document.write( "Look at the point (3,5).  If you double 3 you get 6, and 6 is 1 more than 5.\r\n" );
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document.write( "Look at the point (4,7).  If you double 4 you get 8, and 8 is 1 more than 7.\r\n" );
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document.write( "Look at the point (5,9).  If you double 5 you get 10, and 10 is 1 more than 9.\r\n" );
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document.write( "Now take the general case (x,y) and say the same thing about it:\r\n" );
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document.write( "Look at the point (x,y).  If you double x you get 2x, and 2x is 1 more than y.\r\n" );
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document.write( "Write that as an equation:\r\n" );
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document.write( "                 2x = y + 1\r\n" );
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document.write( "which simplifies to\r\n" );
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document.write( "             2x - 1 = y                    \r\n" );
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document.write( "or \r\n" );
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document.write( "                  y = 2x - 1\r\n" );
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document.write( "Third way:\r\n" );
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document.write( "Look at the point (2,3).  If you subtract 2 from 3 you get 1, and 1 is 1 less than 2.\r\n" );
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document.write( "Look at the point (3,5).  If you subtract 3 from 5 you get 2, and 2 is 1 less than 3.\r\n" );
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document.write( "Look at the point (4,7).  If you subtract 4 from 7 you get 3, and 3 is 1 less than 4.\r\n" );
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document.write( "Look at the point (5,9).  If you subtract 5 from 9 you get 4, and 4 is 1 less than 5.\r\n" );
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document.write( "Now take the general case (x,y) and say the same thing about it:\r\n" );
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document.write( "Look at the point (x,y).  If you subtract x from y you get y-x, and y-x is 1 less than x.\r\n" );
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document.write( "Write that as an equation:\r\n" );
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document.write( "              y-x = x-1\r\n" );
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document.write( "which simplifies to\r\n" );
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document.write( "                y = 2x - 1\r\n" );
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document.write( "There are even other ways to do it but you always get y = 2x - 1\r\n" );
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document.write( "Edwin
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