document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=254318>Question 254318</A>: <I><SPAN STYLE=\"word-break: break-all;\"> What is the value of k if the line 2x + 3y  =  3 is perpendicular to the line 2x + ky + 1  =  0? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #186672 by </B><A HREF=/tutors/aboutme.mpl?userid=vleith><B>vleith(2983)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=vleith><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=186672\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> for two lines to be perpendicular, their slopes have to have a product of -1\r<BR>\n" );
document.write( "\n" );
document.write( "Find the slope of the first line<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x+%2B+3y++=++3+ ALIGN=MIDDLE  ALT=\"2x+%2B+3y++=++3+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3y+=+-2x+%2B+3 ALIGN=MIDDLE  ALT=\"3y+=+-2x+%2B+3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+-%282%2F3%29x+%2B+1 ALIGN=MIDDLE  ALT=\"y+=+-%282%2F3%29x+%2B+1\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "So the slope is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2%2F3 ALIGN=MIDDLE  ALT=\"-2%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "Find the slope of the second line<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x+%2B+ky+%2B+1++=++0 ALIGN=MIDDLE  ALT=\"2x+%2B+ky+%2B+1++=++0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ky+=+-2x+-+1 ALIGN=MIDDLE  ALT=\"ky+=+-2x+-+1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+-%282%2Fk%29x+-1%2Fk ALIGN=MIDDLE  ALT=\"y+=+-%282%2Fk%29x+-1%2Fk\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So the slope of the second line is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2%2Fk ALIGN=MIDDLE  ALT=\"-2%2Fk\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "Set the product of the two slopes equal to -1<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-2%2F3%29+%2A+%28-2%2Fk%29+=+-1 ALIGN=MIDDLE  ALT=\"%28-2%2F3%29+%2A+%28-2%2Fk%29+=+-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2F3k+=+-1 ALIGN=MIDDLE  ALT=\"4%2F3k+=+-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k+=+-4%2F3 ALIGN=MIDDLE  ALT=\"k+=+-4%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "Plot the graphs and verify<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C400%2C-10%2C10%2C-10%2C10%2C+-2x%2F3+%2B1+%2C+3x%2F2+%2B+3%2F4%29 ALIGN=MIDDLE  ALT=\"graph%28400%2C400%2C-10%2C10%2C-10%2C10%2C+-2x%2F3+%2B1+%2C+3x%2F2+%2B+3%2F4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );