document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1049115>Question 1049115</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Determine whether the pair of lines is parallel, perpendicular, or neither.<BR>\n" );
document.write( "X-3y= -2<BR>\n" );
document.write( "Y= 4X - 3 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #664641 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=664641\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> (1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+-+3y+=+-2+ ALIGN=MIDDLE  ALT=\"+x+-+3y+=+-2+\"   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+=+4x+-+3+ ALIGN=MIDDLE  ALT=\"+y+=+4x+-+3+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "------------------<BR>\n" );
document.write( "Put both equations into the <BR>\n" );
document.write( "slope-intercept form which<BR>\n" );
document.write( "will look like:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+m%2Ax+%2B+b+ ALIGN=MIDDLE  ALT=\"+y+=+m%2Ax+%2B+b+\"   DISABLED_style= \"max-width:90%; height:auto;\" > where<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+m+ ALIGN=MIDDLE  ALT=\"+m+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = slope<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+b+ ALIGN=MIDDLE  ALT=\"+b+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = y-intercept<BR>\n" );
document.write( "---------------------------<BR>\n" );
document.write( "Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+ ALIGN=MIDDLE  ALT=\"+x+\"   DISABLED_style= \"max-width:90%; height:auto;\" > from both sides of (1)<BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-3y+=+-x+-+2+ ALIGN=MIDDLE  ALT=\"+-3y+=+-x+-+2+\"   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( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+-x%2F%28-3%29+-+2%2F%28-3%29+ ALIGN=MIDDLE  ALT=\"+y+=+-x%2F%28-3%29+-+2%2F%28-3%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Note that (-)/(-) = (+) ,so<BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+%281%2F3%29%2Ax+%2B+2%2F3+ ALIGN=MIDDLE  ALT=\"+y+=+%281%2F3%29%2Ax+%2B+2%2F3+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----------------------------<BR>\n" );
document.write( "Note that (2) is already in the slope-intercept form<BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+4x+-+3+ ALIGN=MIDDLE  ALT=\"+y+=+4x+-+3+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----------------------<BR>\n" );
document.write( "If these lines were parallel, then their slopes would<BR>\n" );
document.write( "be the same, and they are not<BR>\n" );
document.write( "If these lines were perpendicular, then their slopes<BR>\n" );
document.write( "would have the relation:<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;\" ><BR>\n" );
document.write( "If <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+m%5B1%5D+=+1%2F3+ ALIGN=MIDDLE  ALT=\"+m%5B1%5D+=+1%2F3+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, solve for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+m%5B2%5D+ ALIGN=MIDDLE  ALT=\"+m%5B2%5D+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+1%2F3+=+-1%2Fm%5B2%5D+ ALIGN=MIDDLE  ALT=\"+1%2F3+=+-1%2Fm%5B2%5D+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><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( "But actually, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+m%5B2%5D+=+4+ ALIGN=MIDDLE  ALT=\"+m%5B2%5D+=+4+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so these<BR>\n" );
document.write( "line are neither parallel nor perpendicular<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );