document.write( "Question 117317This question is from textbook Glencoe Geometry
\n" ); document.write( ": Using graph paper, graph the question and plot the given ordered pair. Then construct a perpendicular segment and find the distance from the point to the line.\r
\n" ); document.write( "\n" ); document.write( "26. 3x + 4y = 1, (2, 5)\r
\n" ); document.write( "\n" ); document.write( "The problem I'm having with this is that I have no idea how to solve for x and y...Please help, and thanks in advance!
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Algebra.Com's Answer #86126 by Edwin McCravy(20056)\"\" \"About 
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Using graph paper, graph the question and plot the given ordered pair. Then construct a perpendicular segment and find the distance from the point to the line.
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\n" ); document.write( "The problem I'm having with this is that I have no idea how to solve for x and y...Please help, and thanks in advance!
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document.write( "Arbitrarily choose x = -5 and \r\n" );
document.write( "substitute into\r\n" );
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document.write( "3x + 4y = 1\r\n" );
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document.write( "by replacing x by (-5)\r\n" );
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document.write( "3(-5) + 4y = 1\r\n" );
document.write( "  -15 + 4y = 1\r\n" );
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document.write( "Add 15 to both sides:\r\n" );
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document.write( "       4y = 1+15\r\n" );
document.write( "       4y = 16\r\n" );
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document.write( "Divide both sides by 4\r\n" );
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document.write( "       y = 4\r\n" );
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document.write( "So (-5,4) is a point on the line\r\n" );
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document.write( "Arbitrarily choose x = 7 and \r\n" );
document.write( "substitute into\r\n" );
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document.write( "3x + 4y = 1\r\n" );
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document.write( "by replacing x by (7)\r\n" );
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document.write( "3(7) + 4y = 1\r\n" );
document.write( "   21 + 4y = 1\r\n" );
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document.write( "Add -21 to both sides:\r\n" );
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document.write( "       4y = 1-21\r\n" );
document.write( "       4y = -20\r\n" );
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document.write( "Divide both sides by 4\r\n" );
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document.write( "       y = -5\r\n" );
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document.write( "So (7,-5) is a point on the line\r\n" );
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document.write( "So plot those two points:\r\n" );
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document.write( "Now draw a line through them:\r\n" );
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document.write( "Now plot the point (2,5)\r\n" );
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document.write( "Now construct a perpendicular line from (2,5) to the line\r\n" );
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document.write( "It appears that this perpendicular touches the line at the point\r\n" );
document.write( "(-1,1).  Let's stop and make sure that point really is on the line:\r\n" );
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document.write( "Substituting (x,y) = (-1,1)\r\n" );
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document.write( "     3x + 4y = 1\r\n" );
document.write( "3(-1) + 4(1) = 1\r\n" );
document.write( "      -3 + 4 = 1\r\n" );
document.write( "           1 = 1\r\n" );
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document.write( "Yes (-1,1) is on the line.  So all we need to do is to use\r\n" );
document.write( "the distance formula:\r\n" );
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document.write( "d = Ö(x2-x1)² + (y2-y1)²\r\n" );
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document.write( "where (x1,y1) = (2,5) and (x2,y2) = (-1,1)\r\n" );
document.write( "     ________________\r\n" );
document.write( "d = Ö(-1-2)² + (1-5)²\r\n" );
document.write( "     _____________\r\n" );
document.write( "d = Ö(-3)² + (-4)²\r\n" );
document.write( "     ______\r\n" );
document.write( "d = Ö9 + 16\r\n" );
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document.write( "d = Ö25\r\n" );
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document.write( "d = 5\r\n" );
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document.write( "So the distance is 5 units.\r\n" );
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document.write( "Edwin
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