document.write( "Question 1144940: Please help me: this is the question through (-4,4) and perpendicular to
\n" ); document.write( "2x + 3y=8. Thank you! \n" ); document.write( "
Algebra.Com's Answer #766118 by Edwin McCravy(20055)\"\" \"About 
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Please help me: this is the question through (-4,4) and perpendicular to
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The quick way to solve this type of problem is to learn that the\r\n" );
document.write( "equation of a line:\r\n" );
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document.write( "1. parallel to Ax + By = C through (x1, y1) is\r\n" );
document.write( "   Ax + By = Ax1 + By1\r\n" );
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document.write( "2. perpendicular to Ax + By = C through (x1, y1) is \r\n" );
document.write( "   Bx - Ay = Bx1 - Ay1\r\n" );
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document.write( "So the answer is 3x - 2y = 3(-4) - 2(4)\r\n" );
document.write( "                 3x - 2y = -12 - 8\r\n" );
document.write( "                 3x - 2y = -20\r\n" );
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document.write( "But often this method is not taught.  So we find the slope of\r\n" );
document.write( "2x + 3y = 8 by solving for y to get it into slope-intercept form\r\n" );
document.write( "y = mx + b:\r\n" );
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document.write( "2x + 3y = 8\r\n" );
document.write( "     3y = -2x + 8\r\n" );
document.write( "      y = (-2/3)x + 8/3\r\n" );
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document.write( "Then we compare that to \r\n" );
document.write( "      y = mx + b\r\n" );
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document.write( "and get that the slope m = -2/3. Then we take the reciprocal of the\r\n" );
document.write( "slope and give it the opposite sign, m = +3/2.  Then we use the point-\r\n" );
document.write( "slope form for the equation of a line, which is\r\n" );
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document.write( " y - y1 = m(x - x1)\r\n" );
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document.write( "  y - 4 = (3/2)(x - (-4))\r\n" );
document.write( "  y - 4 = (3/2)(x + 4)\r\n" );
document.write( "Multiply both sides by 2\r\n" );
document.write( " 2y - 8 = 3(x + 4)\r\n" );
document.write( " 2y - 8 = 3x + 12\r\n" );
document.write( "2y - 3x = 20\r\n" );
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document.write( "That's equivalent to the answer using the short method. We multiply\r\n" );
document.write( "through by -1:\r\n" );
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document.write( "-2y + 3x = -20\r\n" );
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document.write( "Then reverse the terms on the left\r\n" );
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document.write( " 3x - 2y = -20\r\n" );
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document.write( "Edwin
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