document.write( "Question 342353: Take a look at the table below and write out an equation for f(x). Show your work.
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Algebra.Com's Answer #245046 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "  x	-3	-2	1	3	4\r\n" );
document.write( "f(x)	0	 3	12	18	21\r\n" );
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document.write( "One way is to plot the points and see what the graph looks like\r\n" );
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document.write( "Hmm!  Looks like a straight line could be drawn through all\r\n" );
document.write( "5 of those points.  I'll get my ruler and green pen and see:\r\n" );
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document.write( "Sure looks like a straight line to me.  So I'll just find the equation\r\n" );
document.write( "of the line that goes through, say, the first two points (any two\r\n" );
document.write( "of the points would do).\r\n" );
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document.write( "(-3,0), (-2,3)\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" );
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document.write( "\"m=%28%283%29-%280%29%29%2F%28%28-2%29-%28-3%29%29\"\r\n" );
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document.write( "\"m=3%2F%28-2%2B3%29\"\r\n" );
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document.write( "\"m=3%2F%28-1%29\"\r\n" );
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document.write( "\"m=3\"\r\n" );
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document.write( "Then I'll substitute that in the point-slope form:\r\n" );
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document.write( "\"y-y%5B1%5D=m%28x-x%5B1%5D%29\"\r\n" );
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document.write( "\"y-0=3%28x-%28-3%29%29\"\r\n" );
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document.write( "\"y=3%28x%2B3%29\"\r\n" );
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document.write( "\"y=3x%2B9\"\r\n" );
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document.write( "That's the answer.\r\n" );
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document.write( "Let's check to see if it works with all 5 points:\r\n" );
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document.write( "Substituting (-3,0)\r\n" );
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document.write( "\"y=3x%2B9\"\r\n" );
document.write( "\"0=3%28-3%29%2B9\"\r\n" );
document.write( "\"0=-9%2B9\"\r\n" );
document.write( "\"0=0\"\r\n" );
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document.write( "Substituting (-2,3)\r\n" );
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document.write( "\"y=3x%2B9\"\r\n" );
document.write( "\"3=3%28-2%29%2B9\"\r\n" );
document.write( "\"3=-6%2B9\"\r\n" );
document.write( "\"3=3\"\r\n" );
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document.write( "Substituting (1,12)\r\n" );
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document.write( "\"y=3x%2B9\"\r\n" );
document.write( "\"12=3%281%29%2B9\"\r\n" );
document.write( "\"12=3%2B9\"\r\n" );
document.write( "\"12=12\"\r\n" );
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document.write( "Substituting (3,18)\r\n" );
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document.write( "\"y=3x%2B9\"\r\n" );
document.write( "\"18=3%283%29%2B9\"\r\n" );
document.write( "\"18=9%2B9\"\r\n" );
document.write( "\"18=18\"\r\n" );
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document.write( "Substituting (4,21)\r\n" );
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document.write( "\"y=3x%2B9\"\r\n" );
document.write( "\"21=3%284%29%2B9\"\r\n" );
document.write( "\"21=12%2B9\"\r\n" );
document.write( "\"21=21\"\r\n" );
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document.write( "Yeppers, it works for all 5 points,\r\n" );
document.write( "so the equation is \r\n" );
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document.write( "y = 3x + 9\r\n" );
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document.write( "Edwin
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