document.write( "Question 727411: find the equation of the line that has the points (1/4,-1/3),(-1/4,-3).write the equation in standard form \n" ); document.write( "
Algebra.Com's Answer #445093 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "The above solution contains a sign error.\r\n" );
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document.write( "First we use the slope formula:\r\n" );
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document.write( "m = \"%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29\"\r\n" );
document.write( "where (x1,y1) = (\"1%2F4\",\"-1%2F3\").\r\n" );
document.write( "and where (x2,y2) = (\"-1%2F4\",-3).\r\n" );
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document.write( "m = \"%28%28-3%29-%28-1%2F3%29%29%2F%28%28-1%2F4%29-%281%2F4%29%29\" = \"%28-3%2B1%2F3%29%2F%28-1%2F4-1%2F4%29\" = \"-3%2F1%2B1%2F3%29%2F%28-2%2F4%29\" = \"%28-9%2F3%2B1%2F3%29%2F-1%2F2%29\" = \"%28-8%2F3%29%2F%28-1%2F2%29\" = \"expr%28-8%2F3%29%2Aexpr%28-2%2F1%29\" = \"16%2F3\"\r\n" );
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document.write( "Next we use the point slope formula: \r\n" );
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document.write( "Point-slope formula:\r\n" );
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document.write( "y - y1 = m(x - x1)\r\n" );
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document.write( "where (x1,y1) = (\"1%2F4\",\"-1%2F3\"), m = \"16%2F3\"\r\n" );
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document.write( "y - \"-1%2F3\" =  \"16%2F3\"(x - \"1%2F4\")\r\n" );
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document.write( "y + \"1%2F3\" =  \"16%2F3\"(x - \"1%2F4\")\r\n" );
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document.write( "Multiply through by 3\r\n" );
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document.write( "3y + 1 = 16(x - \"1%2F4\")\r\n" );
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document.write( "3y + 1 = 16x - 4\r\n" );
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document.write( "-16x + 3y = -5\r\n" );
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document.write( "Multiply through by -1\r\n" );
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document.write( "16x - 3y = 5\r\n" );
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document.write( "Here is another way to do it:\r\n" );
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document.write( "Substitute both points in \r\n" );
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document.write( "y = mx + b\r\n" );
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document.write( "Substituting (x,y) = (\"1%2F4\",\"-1%2F3\"). \r\n" );
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document.write( "\"-1%2F3\" = m\"%281%2F4%29\" + b\r\n" );
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document.write( "Simplify by multiplying through by LCD = 12\r\n" );
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document.write( "-4 = 3m + 12b\r\n" );
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document.write( "Substituting (x,y) = (\"-1%2F4\",-3). \r\n" );
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document.write( "-3 = m\"%28-1%2F4%29\" + b\r\n" );
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document.write( "Simplify by multiplying through by LCD = 4\r\n" );
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document.write( "-12 = -m + 4b\r\n" );
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document.write( "So you have the system of equations:\r\n" );
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document.write( " -4 = 3m + 12b\r\n" );
document.write( "-12 = -m +  4b\r\n" );
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document.write( "Multiply the bottom equation through by 3 to make the m\r\n" );
document.write( "terms cancel, then add the equations term by term:\r\n" );
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document.write( " -4 =  3m + 12b\r\n" );
document.write( "-36 = -3m + 12b\r\n" );
document.write( "---------------\r\n" );
document.write( "-40 =       24b\r\n" );
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document.write( "\"-40%2F24\" = b\r\n" );
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document.write( "\"-5%2F3\" = b\r\n" );
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document.write( " -4 = 3m + 12b\r\n" );
document.write( "-12 = -m +  4b\r\n" );
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document.write( "Multiply the bottom equation through by -3 to make the b\r\n" );
document.write( "terms cancel, then add the equations term by term:\r\n" );
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document.write( " -4 = 3m + 12b\r\n" );
document.write( " 36 = 3m - 12b\r\n" );
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document.write( " 32 = 6m\r\n" );
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document.write( "\"32%2F6\" = m\r\n" );
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document.write( "\"16%2F3\" = m\r\n" );
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document.write( "So the equation in y-intercept form is\r\n" );
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document.write( "y = \"16%2F3\"x +  \"-5%2F3\"\r\n" );
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document.write( "y = \"16%2F3\"x -  \"5%2F3\"\r\n" );
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document.write( " 3y = 16x - 5\r\n" );
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document.write( "-16x + 3y = -5\r\n" );
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document.write( " 16x - 3y = 5\r\n" );
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document.write( "Edwin

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