document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1186115>Question 1186115</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The line 3kx + 8y = 5 is perpendicular to the line 6y - 4kx = -1. Find k. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #816980 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=816980\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "The line <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3kx+%2B+8y+=+5 ALIGN=MIDDLE  ALT=\"3kx+%2B+8y+=+5\"   DISABLED_style= \"max-width:90%; height:auto;\" > is perpendicular to the line <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6y+-+4kx+=+-1 ALIGN=MIDDLE  ALT=\"6y+-+4kx+=+-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( " 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;\" >.\r<BR>\n" );
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document.write( "write both lines in slope intercept form:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3kx+%2B+8y+=+5 ALIGN=MIDDLE  ALT=\"3kx+%2B+8y+=+5\"   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=8y+=+-3kx++%2B5 ALIGN=MIDDLE  ALT=\"8y+=+-3kx++%2B5\"   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+=+-%283k%2F8%29x++%2B5%2F8 ALIGN=MIDDLE  ALT=\"y+=+-%283k%2F8%29x++%2B5%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" >=> a slope is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m1=-%283k%2F8%29 ALIGN=MIDDLE  ALT=\"m1=-%283k%2F8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6y+-+4kx+=+-1 ALIGN=MIDDLE  ALT=\"6y+-+4kx+=+-1\"   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+=4kx+-1 ALIGN=MIDDLE  ALT=\"6y+=4kx+-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=%284k%2F6%29x+-1%2F6 ALIGN=MIDDLE  ALT=\"y+=%284k%2F6%29x+-1%2F6\"   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+=%282k%2F3%29x+-1%2F6 ALIGN=MIDDLE  ALT=\"y+=%282k%2F3%29x+-1%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" >=> a slope is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m2=%282k%2F3%29 ALIGN=MIDDLE  ALT=\"m2=%282k%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "recall that  perpendicular lines have a slopes negative reciprocal to each other\r<BR>\n" );
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document.write( "so, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m2=-1%2Fm1 ALIGN=MIDDLE  ALT=\"m2=-1%2Fm1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "then\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282k%2F3%29=-1%2F%28-3k%2F8%29 ALIGN=MIDDLE  ALT=\"%282k%2F3%29=-1%2F%28-3k%2F8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282k%2F3%29=1%2F%283k%2F8%29 ALIGN=MIDDLE  ALT=\"%282k%2F3%29=1%2F%283k%2F8%29\"   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=2k%283k%2F8%29=1%2A3 ALIGN=MIDDLE  ALT=\"2k%283k%2F8%29=1%2A3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k%283k%2F4%29=3 ALIGN=MIDDLE  ALT=\"k%283k%2F4%29=3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283k%5E2%29%2F4=3 ALIGN=MIDDLE  ALT=\"%283k%5E2%29%2F4=3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3k%5E2=3%2A4 ALIGN=MIDDLE  ALT=\"3k%5E2=3%2A4\"   DISABLED_style= \"max-width:90%; height:auto;\" >...simplify\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k%5E2=4 ALIGN=MIDDLE  ALT=\"k%5E2=4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k=sqrt%284%29 ALIGN=MIDDLE  ALT=\"k=sqrt%284%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 ALIGN=MIDDLE  ALT=\"k=2\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k=-2 ALIGN=MIDDLE  ALT=\"k=-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "then, your lines are:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+-%28%283%2A2%29%2F8%29x++%2B5%2F8 ALIGN=MIDDLE  ALT=\"y+=+-%28%283%2A2%29%2F8%29x++%2B5%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+-%283%2F4%29x++%2B5%2F8 ALIGN=MIDDLE  ALT=\"y+=+-%283%2F4%29x++%2B5%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=%28%282%2A2%29%2F3%29x+-1%2F6 ALIGN=MIDDLE  ALT=\"y+=%28%282%2A2%29%2F3%29x+-1%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=%284%2F3%29x+-1%2F6 ALIGN=MIDDLE  ALT=\"y+=%284%2F3%29x+-1%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "or\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+-%28%283%2A-2%29%2F8%29x++%2B5%2F8 ALIGN=MIDDLE  ALT=\"y+=+-%28%283%2A-2%29%2F8%29x++%2B5%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%283%2F4%29x++%2B5%2F8 ALIGN=MIDDLE  ALT=\"y+=+%283%2F4%29x++%2B5%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=%28%282%2A-2%29%2F3%29x+-1%2F6 ALIGN=MIDDLE  ALT=\"y+=%28%282%2A-2%29%2F3%29x+-1%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=-%284%2F3%29x+-1%2F6 ALIGN=MIDDLE  ALT=\"y+=-%284%2F3%29x+-1%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<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+-%283%2F4%29x++%2B5%2F8%2C+%284%2F3%29x+-1%2F6%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "or\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+%283%2F4%29x++%2B5%2F8%2C+-%284%2F3%29x+-1%2F6%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );