document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=57851>Question 57851</A>: <I><SPAN STYLE=\"word-break: break-all;\"> decide whether lnes p1 and p2 are perpendicular:\r<BR>\n" );
document.write( "\n" );
document.write( "line p1:y= 3x + 5<BR>\n" );
document.write( "line p2: y= 1/3x + 5 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #39529 by </B><A HREF=/tutors/aboutme.mpl?userid=funmath><B>funmath(2933)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=funmath><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=39529\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> decide whether lnes p1 and p2 are perpendicular:\r<BR>\n" );
document.write( "\n" );
document.write( "line p1:y= <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%283%29 ALIGN=MIDDLE  ALT=\"highlight%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >x + 5<BR>\n" );
document.write( "line p2: y= <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%281%2F3%29 ALIGN=MIDDLE  ALT=\"highlight%281%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >x + 5<BR>\n" );
document.write( "Perpendicular lines have slopes that are negative reciprocals of each other (opposite signs and upside down).<BR>\n" );
document.write( "The slope intercept form of a line is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28y=mx%2Bb%29 ALIGN=MIDDLE  ALT=\"highlight%28y=mx%2Bb%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, where m is the slope and (0,b) is the y-intercept.<BR>\n" );
document.write( ":<BR>\n" );
document.write( "p1 has a slope of, m=3<BR>\n" );
document.write( "p2 has a slope of, m=1/3<BR>\n" );
document.write( ":<BR>\n" );
document.write( "They are upsides down form each other, but they are NOT opposite signs from each other, therefore they are NOT perpendicular.<BR>\n" );
document.write( "Graphically, here's what they look like.  They are not intersecting at right angles:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C200%2C-15%2C15%2C-10%2C10%2C3x%2B5%2C%281%2F3%29x%2B5%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C200%2C-15%2C15%2C-10%2C10%2C3x%2B5%2C%281%2F3%29x%2B5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Happy Calculating!!! </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );