document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=911963>Question 911963</A>: <I><SPAN STYLE=\"word-break: break-all;\"> For what value of k  are the graphs of 12y=-3x+8 and 6y=kx-5 perpendicular? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #553467 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=553467\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> For what value of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k ALIGN=MIDDLE  ALT=\"k\"   DISABLED_style= \"max-width:90%; height:auto;\" > are the graphs of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12y=-3x%2B8 ALIGN=MIDDLE  ALT=\"12y=-3x%2B8\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6y=kx-5 ALIGN=MIDDLE  ALT=\"6y=kx-5\"   DISABLED_style= \"max-width:90%; height:auto;\" > perpendicular?\r<BR>\n" );
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document.write( "the lines are perpendicular if slopes  have opposite signs, and their values are reciprocals\r<BR>\n" );
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document.write( "or, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m%5B1%5D=-1%2Fm%5B2%5D ALIGN=MIDDLE  ALT=\"m%5B1%5D=-1%2Fm%5B2%5D\"   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=12y=-3x%2B8 ALIGN=MIDDLE  ALT=\"12y=-3x%2B8\"   DISABLED_style= \"max-width:90%; height:auto;\" > ...find the slope\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-%283%2F12%29x%2B8%2F12 ALIGN=MIDDLE  ALT=\"y=-%283%2F12%29x%2B8%2F12\"   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=y=+-%281%2F4%29x%2B2%2F3+ ALIGN=MIDDLE  ALT=\"y=+-%281%2F4%29x%2B2%2F3+\"   DISABLED_style= \"max-width:90%; height:auto;\" > .... slope <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m%5B1%5D=+-%283%2F12%29+ ALIGN=MIDDLE  ALT=\"m%5B1%5D=+-%283%2F12%29+\"   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=6y=kx-5 ALIGN=MIDDLE  ALT=\"6y=kx-5\"   DISABLED_style= \"max-width:90%; height:auto;\" > ...find the slope\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28k%2F6%29x-5%2F6 ALIGN=MIDDLE  ALT=\"y=%28k%2F6%29x-5%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" >.... slope <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m%5B2%5D=+%28k%2F6%29+ ALIGN=MIDDLE  ALT=\"m%5B2%5D=+%28k%2F6%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "now find <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k ALIGN=MIDDLE  ALT=\"k\"   DISABLED_style= \"max-width:90%; height:auto;\" > that will make <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m%5B1%5D=-1%2Fm%5B2%5D ALIGN=MIDDLE  ALT=\"m%5B1%5D=-1%2Fm%5B2%5D\"   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=-%283%2F12%29+=-1%2F+%28k%2F6%29+ ALIGN=MIDDLE  ALT=\"-%283%2F12%29+=-1%2F+%28k%2F6%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > ....solve for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k ALIGN=MIDDLE  ALT=\"k\"   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=-%283%2F12%29+=-6%2Fk+ ALIGN=MIDDLE  ALT=\"-%283%2F12%29+=-6%2Fk+\"   DISABLED_style= \"max-width:90%; height:auto;\" > ...cross multiply\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3k+=-6%2A12+ ALIGN=MIDDLE  ALT=\"-3k+=-6%2A12+\"   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=k+=-%286%2A12%29%2F-3+ ALIGN=MIDDLE  ALT=\"k+=-%286%2A12%29%2F-3+\"   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=k+=%28cross%286%292%2A12%29%2Fcross%283%29+ ALIGN=MIDDLE  ALT=\"k+=%28cross%286%292%2A12%29%2Fcross%283%29+\"   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=k+=2%2A12+ ALIGN=MIDDLE  ALT=\"k+=2%2A12+\"   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=highlight%28k+=24%29+ ALIGN=MIDDLE  ALT=\"highlight%28k+=24%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "then <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m%5B2%5D=+%28k%2F6%29+ ALIGN=MIDDLE  ALT=\"m%5B2%5D=+%28k%2F6%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m%5B2%5D=+24%2F6=4+ ALIGN=MIDDLE  ALT=\"m%5B2%5D=+24%2F6=4+\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%2824%2F6%29x-5%2F6 ALIGN=MIDDLE  ALT=\"y=%2824%2F6%29x-5%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" >=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=+4x-5%2F6+ ALIGN=MIDDLE  ALT=\"y=+4x-5%2F6+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "so, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=+-%281%2F4%29x%2B2%2F3+ ALIGN=MIDDLE  ALT=\"y=+-%281%2F4%29x%2B2%2F3+\"   DISABLED_style= \"max-width:90%; height:auto;\" > will be perpendicular to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28k%2F6%29x-5%2F6 ALIGN=MIDDLE  ALT=\"y=%28k%2F6%29x-5%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" > if  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28k+=24%29+ ALIGN=MIDDLE  ALT=\"highlight%28k+=24%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "let see it on a graph:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+4x-5%2F6%2C+-%281%2F4%29x%2B2%2F3%29+ ALIGN=MIDDLE  ALT=\"+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+4x-5%2F6%2C+-%281%2F4%29x%2B2%2F3%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );