document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=27185>Question 27185</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 25.	Are the following lines parallel, perpendicular, or neither?<BR>\n" );
document.write( "   L1 with equation x – 3y = 12<BR>\n" );
document.write( "   L2 with equation 3x + y = 3<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #14775 by </B><A HREF=/tutors/aboutme.mpl?userid=rodriguezh2><B>rodriguezh2(15)</B></A><img src=\"/images/stars/stars-06.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rodriguezh2><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=14775\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Whenever you have this type of problem you must make sure both equations are in y = mx + b form.  Remember m = slope and b = (y)intercept.\r<BR>\n" );
document.write( "\n" );
document.write( "L1 with equation x - 3y = 12 becomes y = (x/3) - 4<BR>\n" );
document.write( "L2 with equation 3x + y = 3 becomes y = -3x +3\r<BR>\n" );
document.write( "\n" );
document.write( "Parallel lines have the same slope.  Therefore the m from L1 and the m from L2 must be equal.  We see that (x/3) does not equal -3x so these two lines cannot be parallel.\r<BR>\n" );
document.write( "\n" );
document.write( "Perpendicular lines have negative (-) reciprocal slope. <BR>\n" );
document.write( "( ex: 2x and -(1/2)x.)<BR>\n" );
document.write( " Since m = (x/3) from L1 and m = -3x in L2 we can say that these are negative reciprocals and so therefore these two lines are perpendicular. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );