document.write( "Question 65750: determine the ratio in which the line joining (0,7) and (-2,1)is
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Algebra.Com's Answer #46469 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
determine the ratio in which the line joining (0,7) and (-2,1)is \r\n" );
document.write( "divided by the line 2x+y-4=0\r\n" );
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document.write( "Nate above took it that you wanted the ratio of the slopes. I think\r\n" );
document.write( "you wanted the ratio in which the line divides the segment.\r\n" );
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document.write( "Here's a graph of the line segment joining (0,7) and (-2,1) in red\r\n" );
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document.write( "Now we'll add the graph of 2x + y - 4 = 0 in green\r\n" );
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document.write( "We want to know into what ratio the green line divides the red \r\n" );
document.write( "line segment.\r\n" );
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document.write( "Plan:\r\n" );
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document.write( "1. Find the equation of the line joining (0,7) and (-2,1)\r\n" );
document.write( "2. Solve the system of equations consisting of the results \r\n" );
document.write( "   of step 1 and line 2x+y-4=0 to find their point of \r\n" );
document.write( "   intersection.\r\n" );
document.write( "3. Find the distances from the point found in step 3 to \r\n" );
document.write( "   (0,7) and (-2,1) \r\n" );
document.write( "4. Find the ratio of these two distances.\r\n" );
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document.write( "1. Find the slope, m:\r\n" );
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document.write( "     y2 - y1\r\n" );
document.write( "m = —————————\r\n" );
document.write( "     x2 - x1\r\n" );
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document.write( "where (x1, y1) = (0,7) and (x2, y2) = (-2,1)\r\n" );
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document.write( "     (1) - (7)     -6     \r\n" );
document.write( "m = ——————————— = ———— = 3\r\n" );
document.write( "     (-2) - (0)    -2      \r\n" );
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document.write( "Now substitute in the point slope formula:\r\n" );
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document.write( "y - y1 = m(x - x1)\r\n" );
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document.write( "y - 7 = 3(x - 0)\r\n" );
document.write( "y - 7 = 3x\r\n" );
document.write( "    y = 3x + 7\r\n" );
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document.write( "2. Solve the system:\r\n" );
document.write( "  \r\n" );
document.write( "    2x + y - 4 = 0\r\n" );
document.write( "    y = 3x + 7\r\n" );
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document.write( "You can do this by substitution.  \r\n" );
document.write( "Point of intersection = (-3/5, 26/5) = (-.6, 5.2)\r\n" );
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document.write( "3. Use the distance formula\r\n" );
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document.write( "   d = Ö(x2 - x1)2+(y2 - y1)2\r\n" );
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document.write( " to find the distance from (0,7) to (-.6, 5.2)\r\n" );
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document.write( "        _____________________\r\n" );
document.write( "   d = Ö(-.6 - 0)2+(5.2 - 7)2\r\n" );
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document.write( "   d = Ö.36 + 3.24\r\n" );
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document.write( "   d = Ö3.6\r\n" );
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document.write( "Also use it to find the distance from (-.6, 5.2) to (-2,1)\r\n" );
document.write( "        _________________________\r\n" );
document.write( "   d = Ö(-2 - (-.6) )2+(1 - 5.2)2\r\n" );
document.write( "        ____________________\r\n" );
document.write( "   d = Ö(-2 + .6)2 + (-4.2)2\r\n" );
document.write( "        _______________\r\n" );
document.write( "   d = Ö(-1.4)2 + 17.64\r\n" );
document.write( "        ____________ \r\n" );
document.write( "   d = Ö1.96 + 17.64\r\n" );
document.write( "        ____\r\n" );
document.write( "   d = Ö19.6\r\n" );
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document.write( "4. The ratio of the two distances \"longer to shorter\" is\r\n" );
document.write( "    ____     ___\r\n" );
document.write( "i  Ö19.6 to Ö3.6, which can be\r\n" );
document.write( "   expressed as a fraction\r\n" );
document.write( "     ________     ______    ___  __\r\n" );
document.write( "    Ö19.6/3.6  = Ö196/36 = Ö196/Ö36 = 14/6 = 7/3 or 7 to 3 or 7:3.\r\n" );
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document.write( "The ratio \"shorter to longer\" is 3 to 7 or 3:7\r\n" );
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document.write( "Edwin
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