document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=374054>Question 374054</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the equation of the bisector of the pair of acute angles formed by the lines 4x-3y= 8 and 2x+y=4 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #266411 by </B><A HREF=/tutors/aboutme.mpl?userid=Alan3354><B>Alan3354(69443)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Alan3354><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=Alan3354><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=266411\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Find the intersection of the 2 lines, = (2,0)<BR>\n" );
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document.write( "Find the slope of the 2 lines:<BR>\n" );
document.write( "4x-3y = 8 m1 = 4/3<BR>\n" );
document.write( "2x+y = 4 m2 = -2<BR>\n" );
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document.write( "The slope is the arctan of the angle the line makes with the x-axis<BR>\n" );
document.write( "arctan(4/3) =~ 53.13º<BR>\n" );
document.write( "arctan(-2) =~ -63.435º<BR>\n" );
document.write( "The angle between them is 116.565º (in Quad 1), so the acute angles are 83.435º<BR>\n" );
document.write( "The bisector makes and angle of 53.15 + (83.435)/2 = 84.8675º with the x-axis<BR>\n" );
document.write( "Its slope = tan(84.8675) = 11.133<BR>\n" );
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document.write( "Use y = mx + b and the point (2,0)<BR>\n" );
document.write( "0 = 2*11.133 + b<BR>\n" );
document.write( "b = -22.266<BR>\n" );
document.write( "Equation is y = 11.133x - 22.266<BR>\n" );
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