document.write( "Question 683826: A pencil of lines described by y=mx+3m-2 \n" ); document.write( "

Algebra.Com's Answer #423782 by Edwin McCravy(20060) $\"\"$ $\"About$

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y=mx+3m-2
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document.write( "Let m=a\r\n" );
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document.write( "y  = a + 3a - 2\r\n" );
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document.write( "let m=b where a and b are not equal.\r\n" );
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document.write( "y = bx + 3b - 2\r\n" );
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document.write( "Solve the system:\r\n" );
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document.write( "ax + 3a - 2 = bx + 3b - 2\r\n" );
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document.write( "ax - bx = -3a + 3b\r\n" );
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document.write( "x(a - b) = -3(a - b)\r\n" );
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document.write( "Since a is not equal to b we may divide through by (a - b) and\r\n" );
document.write( "get:\r\n" );
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document.write( "x = -3\r\n" );
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document.write( "Substituting in\r\n" );
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document.write( "y = ax + 3a - 2\r\n" );
document.write( "y = a(-3) + 3a - 2\r\n" );
document.write( "y = -3a + 3a - 2\r\n" );
document.write( "y = -2\r\n" );
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document.write( "So we have a pencil of lines all going through the point (x,y) = (-3,-2).\r\n" );
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document.write( "[However the pencil of lines does not include the vertical line \r\n" );
document.write( "through (-3,-2) because there is no way to get the equation x=-3 \r\n" );
document.write( "from the equation y = mx + 3m - 2, by substituting a value for m] \r\n" );
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document.write( "Edwin

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