document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=189764>Question 189764</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Decide whether the pair of lines is parallel, perpendicular or neither. <BR>\n" );
document.write( "3x+5y=3<BR>\n" );
document.write( "5x+3y=4 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #142383 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=142383\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> There are actually (4) possibilities when given 2 equations<BR>\n" );
document.write( "---------------<BR>\n" );
document.write( "(1) They could actually be the SAME line<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x+%2B+2y+=+8 ALIGN=MIDDLE  ALT=\"3x+%2B+2y+=+8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6x+%2B+4y+=+16 ALIGN=MIDDLE  ALT=\"6x+%2B+4y+=+16\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "These are the same line because one is an<BR>\n" );
document.write( "exact multiple of the other<BR>\n" );
document.write( "---------------<BR>\n" );
document.write( "(2) They can be parallel lines<BR>\n" );
document.write( "If the slope of  DISABLED_event_one=  the slope of the other<BR>\n" );
document.write( "---------------<BR>\n" );
document.write( "(3) Perpendicular lines<BR>\n" );
document.write( "If the slope of  DISABLED_event_one=  the negative reciprocal<BR>\n" );
document.write( "of the slope of the other<BR>\n" );
document.write( "---------------<BR>\n" );
document.write( "(4) Two different lines, neither parallel nor perpendicular<BR>\n" );
document.write( "----------------<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x+%2B+5y+=+3 ALIGN=MIDDLE  ALT=\"3x+%2B+5y+=+3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x+%2B+3y+=+4 ALIGN=MIDDLE  ALT=\"5x+%2B+3y+=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "These need to be put in the slope-intercept form<BR>\n" );
document.write( "which is: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+mx+%2B+b ALIGN=MIDDLE  ALT=\"y+=+mx+%2B+b\"   DISABLED_style= \"max-width:90%; height:auto;\" > (m is the slope)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x+%2B+5y+=+3 ALIGN=MIDDLE  ALT=\"3x+%2B+5y+=+3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x ALIGN=MIDDLE  ALT=\"3x\"   DISABLED_style= \"max-width:90%; height:auto;\" > from both sides<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5y+=+-3x+%2B+3 ALIGN=MIDDLE  ALT=\"5y+=+-3x+%2B+3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Divide both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5 ALIGN=MIDDLE  ALT=\"5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+-%283%2F5%29x+%2B+3 ALIGN=MIDDLE  ALT=\"y+=+-%283%2F5%29x+%2B+3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Notice that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m+=+-3%2F5 ALIGN=MIDDLE  ALT=\"m+=+-3%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "----------------<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x+%2B+3y+=+4 ALIGN=MIDDLE  ALT=\"5x+%2B+3y+=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x ALIGN=MIDDLE  ALT=\"5x\"   DISABLED_style= \"max-width:90%; height:auto;\" > from both sides<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3y+=+-5x+%2B+4 ALIGN=MIDDLE  ALT=\"3y+=+-5x+%2B+4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Divide both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"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+=+-%285%2F3%29x+%2B+4 ALIGN=MIDDLE  ALT=\"y+=+-%285%2F3%29x+%2B+4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Notice <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m+=+-5%2F3 ALIGN=MIDDLE  ALT=\"m+=+-5%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "If this slope was 5/3, it would be perpendicular<BR>\n" );
document.write( "to the other line.<BR>\n" );
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document.write( "These two lines are neither the same line, parallel, or<BR>\n" );
document.write( "perpendicular. I'll plot them:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C+-%283%2F5%29x+%2B+3%2C+-%285%2F3%29x+%2B+4%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );