document.write( "Question 313871: Graph the triangle enclosed by the Y-axis and the graphs of y - 3x = -2 and y + 3x = 2 Find the area of the triangle. \n" ); document.write( "
Algebra.Com's Answer #224413 by Edwin McCravy(20056)\"\" \"About 
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Graph the triangle enclosed by the Y-axis and the
\n" ); document.write( "graphs of y - 3x = -2 and y + 3x = 2
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document.write( "Draw the graphs of the lines:\r\n" );
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document.write( "\"system%28y-3x=-2%2Cy%2B3x=2%29\"\r\n" );
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document.write( "First put them in slope intercept form:\r\n" );
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document.write( "\"system%28y=3x-2%2Cy=-3x%2B2%29\"\r\n" );
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document.write( "Their y-intercepts are (0,-2) and (0,2) respectively,\r\n" );
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document.write( "So these are two of the vertices of the triangle we wish\r\n" );
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document.write( "to find the area of. \r\n" );
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document.write( "We solve the system of equations to find the coordinates\r\n" );
document.write( "wheteh they intersect, which be the third vertex of the\r\n" );
document.write( "triangle we wish to find the area of.\r\n" );
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document.write( "\"system%28y=3x-2%2Cy=-3x%2B2%29\"\r\n" );
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document.write( "Set the values of y equal:\r\n" );
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document.write( "\"3x-2=-3x%2B2\"\r\n" );
document.write( "\"6x=4\"\r\n" );
document.write( "\"x=2%2F3\"\r\n" );
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document.write( "Substituting in \r\n" );
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document.write( "\"y=3x-2\"\r\n" );
document.write( "\"y=3%282%2F3%29-2\"\r\n" );
document.write( "\"y=cross%283%29%282%2Fcross%283%29%29-2%0D%0A%7B%7B%7By=2-2\"\r\n" );
document.write( "\"y=0\"\r\n" );
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document.write( "So the third point of the triangle is (0,\"2%2F3\")\r\n" );
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document.write( "\"system%28y=3x-2%2Cy=-3x%2B2%29\"\r\n" );
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document.write( "Draw the graphs of the lines\r\n" );
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document.write( "So we wish to find the area of this triangle:\r\n" );
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document.write( "Take as a base b the line segement from (0,-2) to (0,2) which is\r\n" );
document.write( "4 units long.  Take as an altitude h the line segment from (0,0) to\r\n" );
document.write( "(\"2%2F3\",0) which is \"2%2F3\" units long.\r\n" );
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document.write( "Area of a triangle is  \r\n" );
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document.write( "A = \"1%2F2\"bh \r\n" );
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document.write( "A = \"1%2F2\"×(4)×(\"2%2F3\")\r\n" );
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document.write( "A = \"1%2Fcross%282%29\"×(4)×(\"cross%282%29%2F3\")\r\n" );
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document.write( "A = \"4%2F3\"\r\n" );
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document.write( "Edwin
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