document.write( "Question 65275: find the equation of the line that passes through the intersection of the given pair of lines and satisfies the other given condition. graph.\r
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Algebra.Com's Answer #45809 by Edwin McCravy(20060)\"\" \"About 
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find the equation of the line that passes through the intersection \r\n" );
document.write( "of the given pair of lines and satisfies the other given condition. \r\n" );
document.write( "graph. \r\n" );
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document.write( "3x + 4y - 2 = 0, 3x - 4y + 1 = 0; the intercepts are equal.\r\n" );
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document.write( "First we must find the point of intersection by \r\n" );
document.write( "the system of two equations in two unknowns\r\n" );
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document.write( "3x + 4y - 2 = 0 \r\n" );
document.write( "3x - 4y + 1 = 0\r\n" );
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document.write( "You can solve that system of equations and get\r\n" );
document.write( " x = 1/6, y = 3/8\r\n" );
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document.write( "Now the problem become:\r\n" );
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document.write( "Find the equation of the line through the point\r\n" );
document.write( "(1/6, 3/8)\r\n" );
document.write( "which has equal intercepts.  To have equal \r\n" );
document.write( "intercept, if the point ehere the line crosses \r\n" );
document.write( "the y-axis is (0, b), then the point where the \r\n" );
document.write( "line crosses the x-axis is (b, 0).\r\n" );
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document.write( "So we find its slope by the slope formula\r\n" );
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document.write( "(x1, y1) = (0, b) and (x2, y2) = (b, 0)\r\n" );
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document.write( "     y2 - y1     (0) - (b)     -b\r\n" );
document.write( "m = --------- = ----------- = ---- = -1 \r\n" );
document.write( "     x2 - x1     (b) - (0)      b\r\n" );
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document.write( "Now we use the point slope form with m = -1 \r\n" );
document.write( "and (x1, y1) = (1/6, 3/8)\r\n" );
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document.write( "y - y1 = m(x - x1) \r\n" );
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document.write( "y - (3/8) = -1(x - 1/6)\r\n" );
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document.write( "y - 3/8 = -x + 1/6\r\n" );
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document.write( "Now we multiply through by LCD = 24 to clear \r\n" );
document.write( "of fractions: \r\n" );
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document.write( "24y - 9 = -24x + 4\r\n" );
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document.write( "24y + 24x - 13 = 0\r\n" );
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document.write( "or solve for y and get\r\n" );
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document.write( "y = -x + 13/24 \r\n" );
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document.write( "The two equal intercepts are at points \r\n" );
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document.write( "(13/24, 0) and (0, 13/24)\r\n" );
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document.write( "Edwin
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