document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=621707>Question 621707</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Determine whether each pair of equations represents perpendicular lines.<BR>\n" );
document.write( "y=5-3x, 3x-y=8\r<BR>\n" );
document.write( "\n" );
document.write( "Thank you,<BR>\n" );
document.write( "Janice </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #390888 by </B><A HREF=/tutors/aboutme.mpl?userid=josmiceli><B>josmiceli(19441)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josmiceli><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=josmiceli><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=390888\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If you have a line that looks like<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+m%2Ax+%2B+b%5B1%5D+ ALIGN=MIDDLE  ALT=\"+y+=+m%2Ax+%2B+b%5B1%5D+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then a line perpendicular to it<BR>\n" );
document.write( "looks like <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+%28-1%2Fm+%29%2Ax+%2B+b%5B2%5D+ ALIGN=MIDDLE  ALT=\"+y+=+%28-1%2Fm+%29%2Ax+%2B+b%5B2%5D+\"   DISABLED_style= \"max-width:90%; height:auto;\" > where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+m+ ALIGN=MIDDLE  ALT=\"+m+\"   DISABLED_style= \"max-width:90%; height:auto;\" > is slope<BR>\n" );
document.write( "-------------<BR>\n" );
document.write( "Your lines are<BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+5+-+3x+ ALIGN=MIDDLE  ALT=\"+y+=+5+-+3x+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3x+-+y=+8+ ALIGN=MIDDLE  ALT=\"+3x+-+y=+8+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "--------------<BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+-3x+%2B+5+ ALIGN=MIDDLE  ALT=\"+y+=+-3x+%2B+5+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and<BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-y+=+-3x+%2B+8+ ALIGN=MIDDLE  ALT=\"+-y+=+-3x+%2B+8+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Multiply both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1 ALIGN=MIDDLE  ALT=\"-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+3x+-+8+ ALIGN=MIDDLE  ALT=\"+y+=+3x+-+8+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----------------<BR>\n" );
document.write( "Now compare the slopes. They are<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+m%5B1%5D+=+-3+ ALIGN=MIDDLE  ALT=\"+m%5B1%5D+=+-3+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+m%5B2%5D+=+3+ ALIGN=MIDDLE  ALT=\"+m%5B2%5D+=+3+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "They can't be perpendicular because<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+m%5B1%5D+=+-m%5B2%5D+ ALIGN=MIDDLE  ALT=\"+m%5B1%5D+=+-m%5B2%5D+\"   DISABLED_style= \"max-width:90%; height:auto;\" > and to be perpendicular,<BR>\n" );
document.write( "<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;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );