document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=893360>Question 893360</A>: <I><SPAN STYLE=\"word-break: break-all;\"> determine the value of k so that the lines kx-y=-1/3 and 3y=1-6x will intersect at one point </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #541221 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39617)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=541221\">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=-y=-kx-1%2F3 ALIGN=MIDDLE  ALT=\"-y=-kx-1%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%28y=kx%2B1%2F3%29 ALIGN=MIDDLE  ALT=\"highlight_green%28y=kx%2B1%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >;\r<BR>\n" );
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document.write( "The second equation is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%28y=-2x%2B1%2F3%29 ALIGN=MIDDLE  ALT=\"highlight_green%28y=-2x%2B1%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "If slopes were equal, k=-2, and these two lines would be the same identical line.  To make them each DIFFERENT lines, then any k such that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k%3C%3E-2 ALIGN=MIDDLE  ALT=\"k%3C%3E-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > will work.  As long as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k%3C%3E-2 ALIGN=MIDDLE  ALT=\"k%3C%3E-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, the two lines will intersect in exactly one point. </SPAN>\n" );
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