document.write( "Question 754176: In the xy plane line l passes through the origin and is perpendicular to the line 4x+y=k, where k is a constant. If the two lines intersect at the point (t, t+1), what is the value of t?\r
\n" ); document.write( "\n" ); document.write( "I don't understand the significance of the line passing through the origin. \r
\n" ); document.write( "\n" ); document.write( "The answer is -4/3 \n" ); document.write( "
Algebra.Com's Answer #458865 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "We put the line\r\n" );
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document.write( "4x + y = k\r\n" );
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document.write( "in slope-intercept form y = mx + b\r\n" );
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document.write( "4x + y = k\r\n" );
document.write( "     y = -4x + k\r\n" );
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document.write( "So it has slope m = -4.\r\n" );
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document.write( "That means that any line perpendicular to it has\r\n" );
document.write( "the slope m = \"1%2F4\", the \"negative reciprocal\"\r\n" );
document.write( "of the -4, i.e., \"invert and change the sign\".\r\n" );
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document.write( "Now we can find the equation of the line through\r\n" );
document.write( "the origin (0,0) with slope \"1%2F4\".\r\n" );
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document.write( "We use the point-slope formula:\r\n" );
document.write( "y - y1 = m(x - x1)\r\n" );
document.write( "where (x1,y1) = (0,0)\r\n" );
document.write( "y - 0 = \"1%2F4\"(x-0)\r\n" );
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document.write( "which simplifies to\r\n" );
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document.write( "y = \"1%2F4\"x\r\n" );
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document.write( "That will be easier to work with if we \r\n" );
document.write( "clear the fraction by multiplying both\r\n" );
document.write( "sides by 4\r\n" );
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document.write( "4y = x \r\n" );
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document.write( "Now we have this system of equations:\r\n" );
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document.write( "     y = -4x + k\r\n" );
document.write( "    4y = x\r\n" );
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document.write( "which we are told it has solution (t,t+1),\r\n" );
document.write( "their given point of intersection.\r\n" );
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document.write( "So we substitute t for x and t+1 for y:\r\n" );
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document.write( "     t+1 = -4t + k\r\n" );
document.write( "    4(t+1) = t\r\n" );
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document.write( "which simplify to:\r\n" );
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document.write( "    5t-k = -1 \r\n" );
document.write( "    4t+4 = t\r\n" );
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document.write( "and the second one simplifies further and we have:\r\n" );
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document.write( "    5t-k = -1\r\n" );
document.write( "      3t = -4\r\n" );
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document.write( "We solve the 2nd equation for t\r\n" );
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document.write( "       t = \"-4%2F3\"\r\n" );
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document.write( "That's all you wanted.  However you can continue and\r\n" );
document.write( "find k too\r\n" );
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document.write( "Substituting \"-4%2F3\" for t the first equation, we have\r\n" );
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document.write( "    5t-k = -1\r\n" );
document.write( "    5(\"-4%2F3\")-k = -1\r\n" );
document.write( "    \"-20%2F3\"-k = -1\r\n" );
document.write( "    -20-3k = -3\r\n" );
document.write( "       -3k = 17\r\n" );
document.write( "         k = \"-17%2F3\"\r\n" );
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document.write( "But all you wanted was  t = \"-4%2F3\"\r\n" );
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document.write( "Edwin
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