document.write( "Question 684155: Find the equation of the line parallel to the line 2x+3y=6 and passing at a distance $\"5sqrt%2813%29%2F13\"$ from the point (-1,1)? Please I need your solution and graph! thank you so much... \n" ); document.write( "

Algebra.Com's Answer #423961 by Edwin McCravy(20055) $\"\"$ $\"About$

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Find the equation of the line parallel to the line 2x+3y=6 and passing at a distance $\"5sqrt%2813%29%2F13\"$ from the point (-1,1)? Please I need your solution and graph! thank you so much...
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document.write( "Here is the graph of the line 2x + 3y = 6 and the point (-1,1):\r\n" );
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document.write( "2x + 3y = 6\r\n" );
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document.write( "is equivalent to\r\n" );
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document.write( "2x + 3y - 6 = 0.\r\n" );
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document.write( "Every line parallel to the line \r\n" );
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document.write( "2x + 3y - 6 = 0 \r\n" );
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document.write( "is of the form\r\n" );
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document.write( "2x + 3y + K = 0.\r\n" );
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document.write( "The distance from the point (p,q) to the line \r\n" );
document.write( "Ax + By + C = 0 is given by the formula:\r\n" );
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document.write( "So since the distance from (-1,1) to the line 2x + 3y + K = 0\r\n" );
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document.write( "is to be , we have\r\n" );
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document.write( "Cross multiply and solve for K, \r\n" );
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document.write( "using the + we get K = 4 and using th - we get -6 \r\n" );
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document.write( "For K = 4 the solution is\r\n" );
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document.write( "2x + 3y + 4 = 0\r\n" );
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document.write( "which has this graph (in green):\r\n" );
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document.write( "using K = -6. we have the solution\r\n" );
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document.write( "2x + 3y + (-6) = 0\r\n" );
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document.write( "2x + 3y - 6 = 0\r\n" );
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document.write( "Wow! That's the GIVEN LINE!!!  As it turns out, the given line \r\n" );
document.write( "was itself  units from the point (-1,1).  \r\n" );
document.write( "However we wanted a line PARALLEL to 2x + 3y - 6 = 0, not that \r\n" );
document.write( "line itself.  So the only solution is\r\n" );
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document.write( "2x + 3y + 4 = 0\r\n" );
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document.write( "Edwin

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