document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=641198>Question 641198</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Determine the bisector of the obtuse angle between the line 2x-3y=2 and x+y=6. Sketch the graph. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #403576 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=403576\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+600%2C600%2C+-10%2C+10%2C+-10%2C+10%2C+-x%2B6%2C+2x%2F3-2%2F3%29+ ALIGN=MIDDLE  ALT=\"+graph%28+600%2C600%2C+-10%2C+10%2C+-10%2C+10%2C+-x%2B6%2C+2x%2F3-2%2F3%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The slope of the bisecting line is NOT the average of the slopes of the two given lines.\r<BR>\n" );
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document.write( "We need to find a point on the line of intersection and its slope. First find the point of intersection of the lines:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x+-+3y+=+2 ALIGN=MIDDLE  ALT=\"2x+-+3y+=+2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+%2B+y+=+6 ALIGN=MIDDLE  ALT=\"x+%2B+y+=+6\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The point of intersection is P(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4 ALIGN=MIDDLE  ALT=\"4\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2 ALIGN=MIDDLE  ALT=\"+2\"   DISABLED_style= \"max-width:90%; height:auto;\" >).\r<BR>\n" );
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document.write( "Find the slopes of the given lines.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m1+=+tan%28alpha%29+=+2%2F3 ALIGN=MIDDLE  ALT=\"m1+=+tan%28alpha%29+=+2%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m2+=+tan%28beta%29+=+-1 ALIGN=MIDDLE  ALT=\"m2+=+tan%28beta%29+=+-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Note that for the first line <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=alpha%3C+45 ALIGN=MIDDLE  ALT=\"alpha%3C+45\"   DISABLED_style= \"max-width:90%; height:auto;\" >°.<BR>\n" );
document.write( "Note that for the second line <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=beta+=+135 ALIGN=MIDDLE  ALT=\"beta+=+135\"   DISABLED_style= \"max-width:90%; height:auto;\" >°.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=beta+-+alpha+%3E+90 ALIGN=MIDDLE  ALT=\"beta+-+alpha+%3E+90\"   DISABLED_style= \"max-width:90%; height:auto;\" >°\r<BR>\n" );
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document.write( "Therefore for the bisecting line of the obtuse angle:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m+=+tan%28%28alpha+%2B+beta%29%2F2%29 ALIGN=MIDDLE  ALT=\"m+=+tan%28%28alpha+%2B+beta%29%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So the bisector of the obtuse angle will be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=near ALIGN=MIDDLE  ALT=\"near\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+vertical ALIGN=MIDDLE  ALT=\"+vertical\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "The equation of the line will be:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+-+2+=+m%28x+-4%29 ALIGN=MIDDLE  ALT=\"y+-+2+=+m%28x+-4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
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