document.write( "Question 841975: Explain how to write a function rule from the table below. Then write a function.\r
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Algebra.Com's Answer #507341 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "X|2  4  6\r\n" );
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document.write( "Y|1  0 -1\r\n" );
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document.write( "We may notice that if we take half of the x's, we get\r\n" );
document.write( "1,2,3, and subtract 2 from them you get -1,0,1, which are \r\n" );
document.write( "the y's with opposite signs.  So we can figure a rule \r\n" );
document.write( "like this\r\n" );
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document.write( "Take half of each x, \r\n" );
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document.write( "\"1%2F2\"x\r\n" );
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document.write( "subtract 2, \r\n" );
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document.write( "\"1%2F2\"x - 2\r\n" );
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document.write( "then multiply by -1\r\n" );
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document.write( "-1[\"1%2F2\"x - 2]\r\n" );
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document.write( "\"-1%2F2\"x + 2\r\n" );
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document.write( "Then we would write\r\n" );
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document.write( "f(x) = \"-1%2F2\"x + 2 \r\n" );
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document.write( "But it takes a lot of thinking and intuition to come up with that\r\n" );
document.write( "doing it that way.\r\n" );
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document.write( "Here's a way that doesn't take so much intuition.\r\n" );
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document.write( "If we plot those three points (2,1), (4,0), (6,-1) on an\r\n" );
document.write( "xy coordinate system, we see that we can draw a line through\r\n" );
document.write( "them\r\n" );
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document.write( "so we take 2 of those points and find the equation of the line that passes\r\n" );
document.write( "through them.  Say (2,1) and (4,0) \r\n" );
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document.write( "Use the slope formula:\r\n" );
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document.write( "m = \"%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29\"\r\n" );
document.write( "where (x1,y1) = (2,1)\r\n" );
document.write( "and where (x2,y2) = (4,0)\r\n" );
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document.write( "m = \"%280-1%29%2F%284-2%29\" = \"-1%2F2\"\r\n" );
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document.write( "Point-slope formula:\r\n" );
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document.write( "y - y1 = m(x - x1)\r\n" );
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document.write( "where (x1,y1) = (2,1)\r\n" );
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document.write( "y - (-1) = \"-1%2F2\"(x - 2)\r\n" );
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document.write( "y + 1 = \"-1%2F2\"x + 1\r\n" );
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document.write( "y = \"-1%2F2\"x + 2\r\n" );
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document.write( "f(x) = \"-1%2F2\"x + 2\r\n" );
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document.write( "Edwin
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