document.write( "Question 1091255: How do you write an equation in the variables x and y for the
\n" ); document.write( "line that passes through the point (18,14) and that is
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Algebra.Com's Answer #705653 by Edwin McCravy(20055)\"\" \"About 
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document.write( "First we find the slope of the line 9x+6y=174\r\n" );
document.write( "by solving it for y to get it in slope-y-intercept form,\r\n" );
document.write( "which is \"y=m%2Ax%2Bb\":\r\n" );
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document.write( "\"9x%2B6y=174\"\r\n" );
document.write( "\"6y=-9x%2B174\"\r\n" );
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document.write( "\"expr%286%2F6%29y=expr%28%28-9%29%2F6%29x%2B174%2F6\"\r\n" );
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document.write( "\"y=expr%28-3%2F2%29x%2B29\"\r\n" );
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document.write( "We compare that to the slope-y-intercept form \r\n" );
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document.write( "\"y=m%2Ax%2Bb\"\r\n" );
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document.write( "we see that the slope is \"-3%2F2\"\r\n" );
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document.write( "Then we remember that perpendicular lines have slopes \r\n" );
document.write( "which are opposite signed reciprocals of each other.\r\n" );
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document.write( "Therefore the slope of a line perpendicular to a line\r\n" );
document.write( "with slope \"-3%2F2\" has slope \"%22%22+%2B+2%2F3\".\r\n" );
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document.write( "Now we use the point-slope formula\r\n" );
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document.write( "\"y-y%5B1%5D=m%28x-x%5B1%5D%29\" with (x1, y1) = (18,14),\r\n" );
document.write( "and \"m=2%2F3\"\r\n" );
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document.write( "\"y-14=expr%282%2F3%29%28x-18%29\"\r\n" );
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document.write( "Multiply both sides by 3 to clear the fraction:\r\n" );
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document.write( "\"3y-42=2%28x-18%29\"\r\n" );
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document.write( "\"3y-42=2x-36\"\r\n" );
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document.write( "\"-2x%2B3y=6\"\r\n" );
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document.write( "We want it to begin with a positive term in x, so that\r\n" );
document.write( "it will be in the same form as the given equation, so we\r\n" );
document.write( "we multiply through by -1 \r\n" );
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document.write( "\"2x-3y=-6\"\r\n" );
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document.write( "The Green line is the graph of the Given line 9x+6y=174.\r\n" );
document.write( "The Red line is the graph of the Required line 2x-3y=-6.\r\n" );
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document.write( "Edwin
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