document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=946203>Question 946203</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the equation of the line bisecting the acute angles formed between lines <BR>\n" );
document.write( "X+7y=6 and x-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 #577882 by </B><A HREF=/tutors/aboutme.mpl?userid=Fombitz><B>Fombitz(32388)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Fombitz><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=Fombitz><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=577882\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B7y=6 ALIGN=MIDDLE  ALT=\"x%2B7y=6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7y=-x%2B6 ALIGN=MIDDLE  ALT=\"7y=-x%2B6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-x%2F7%2B6%2F7 ALIGN=MIDDLE  ALT=\"y=-x%2F7%2B6%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m%5B1%5D=-1%2F7 ALIGN=MIDDLE  ALT=\"m%5B1%5D=-1%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-y=4 ALIGN=MIDDLE  ALT=\"x-y=4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=x-4 ALIGN=MIDDLE  ALT=\"y=x-4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m%5B2%5D=1 ALIGN=MIDDLE  ALT=\"m%5B2%5D=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
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document.write( "To get the angle between the two lines using the slopes use,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=tan%28theta%29=abs%28%28m%5B1%5D-m%5B2%5D%29%2F%281%2Bm%5B1%5Dm%5B2%5D%29%29 ALIGN=MIDDLE  ALT=\"tan%28theta%29=abs%28%28m%5B1%5D-m%5B2%5D%29%2F%281%2Bm%5B1%5Dm%5B2%5D%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=tan%28theta%29=abs%28%281-%28-1%2F7%29%29%2F%281-1%2F7%29%29=%288%2F7%29%2F%286%2F7%29=4%2F3 ALIGN=MIDDLE  ALT=\"tan%28theta%29=abs%28%281-%28-1%2F7%29%29%2F%281-1%2F7%29%29=%288%2F7%29%2F%286%2F7%29=4%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=theta=53.13 ALIGN=MIDDLE  ALT=\"theta=53.13\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "The line <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-y=4 ALIGN=MIDDLE  ALT=\"x-y=4\"   DISABLED_style= \"max-width:90%; height:auto;\" > makes a 45 degree angle with the x-axis.<BR>\n" );
document.write( "So starting from that slope and rotating clockwise by half of 53.13 will get us to the slope of the bisector.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=45-53.13%2F2=18.43 ALIGN=MIDDLE  ALT=\"45-53.13%2F2=18.43\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=tan%2818.43%29 ALIGN=MIDDLE  ALT=\"m=tan%2818.43%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=1%2F3 ALIGN=MIDDLE  ALT=\"m=1%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now find the point of intersection of the two lines,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%2B4%2B7y=6 ALIGN=MIDDLE  ALT=\"y%2B4%2B7y=6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8y=2 ALIGN=MIDDLE  ALT=\"8y=2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=1%2F4 ALIGN=MIDDLE  ALT=\"y=1%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Then,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-1%2F4=16%2F4 ALIGN=MIDDLE  ALT=\"x-1%2F4=16%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=17%2F4 ALIGN=MIDDLE  ALT=\"x=17%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now use the point-slope form of a line,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-1%2F4=%281%2F3%29%28x-17%2F4%29 ALIGN=MIDDLE  ALT=\"y-1%2F4=%281%2F3%29%28x-17%2F4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28y=x%2F3-7%2F6%29 ALIGN=MIDDLE  ALT=\"highlight%28y=x%2F3-7%2F6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C300%2C-2%2C8%2C-5%2C5%2Cgrid%281%29%2Ccircle%2817%2F4%2C1%2F4%2C0.25%29%2Cgraph%28300%2C300%2C-2%2C8%2C-5%2C5%2C-x%2F7%2B6%2F7%2Cx-4%2Cx%2F3-7%2F6%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );