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You can put this solution on YOUR website!
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document.write( "That's no explanation at all! It's just a magic trick\r\n" );
document.write( "method that works.\r\n" );
document.write( "9x - 3y = -18\r\n" );
document.write( "{His magic trick: Swap the letters on the\r\n" );
document.write( "left \r\n" );
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document.write( "9y - 3x \r\n" );
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document.write( "change one of the signs, \r\n" );
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document.write( "9y + 3x\r\n" );
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document.write( "substitute in\r\n" );
document.write( "the point (1,5) \r\n" );
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document.write( "9(5) + 3(1) = 45 + 3 = 48\r\n" );
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document.write( "set 9y + 3x equal to 48\r\n" );
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document.write( "9y + 3x = 48\r\n" );
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document.write( "Divided through by 3\r\n" );
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document.write( "3y + x = 16\r\n" );
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document.write( "and abracadabra, you have the answer!\r\n" );
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document.write( "But that's math-a-magic!, not mathematics.\r\n" );
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document.write( "We are given a point (1,5) and the equation of a line that we \r\n" );
document.write( "can easily graph by finding its intercepts (-2,0) and (0,6).\r\n" );
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document.write( "like this:\r\n" );
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document.write( "and we want a line that goes through the given point\r\n" );
document.write( "that is perpendicular to the given line. In other words,\r\n" );
document.write( "we want this red line:\r\n" );
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document.write( "The given line has equation\r\n" );
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document.write( "We get it in slope-intercept form by solving\r\n" );
document.write( "for y:\r\n" );
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document.write( "Divide through by -3\r\n" );
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document.write( "Compare that to\r\n" );
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document.write( "So the given line's slope is m=3.\r\n" );
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document.write( "m=3/1 has a rise of 3 and a run of 1. The slope is\r\n" );
document.write( "positive so it slopes uphill to the right.\r\n" );
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document.write( "A line perpendicular to it will have the rise and\r\n" );
document.write( "run swapped but it will slope downhill to the right.\r\n" );
document.write( "So its slope will have the run and rise swapped as\r\n" );
document.write( "1/3 and will be negative because it slants downhill\r\n" );
document.write( "to the right. So its slope is -1/3.\r\n" );
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document.write( "Then we use the point-slope formula:\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 m=-1/3 and (x1,y1) = (1,5)\r\n" );
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document.write( "Multiply through by LCD = 3\r\n" );
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document.write( "Add x to both sides and then 15 to both sides:\r\n" );
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document.write( "Same as with the magic trick.\r\n" );
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document.write( "Edwin \n" );
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