document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=154830>Question 154830</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The lines px+4y-2=0 and 2x-y+p=0 are perpendicular. Find the value of p. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #114017 by </B><A HREF=/tutors/aboutme.mpl?userid=Earlsdon><B>Earlsdon(6294)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Earlsdon><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=114017\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If the lines are perpendicular, then their slopes are negative reciprocals.<BR>\n" );
document.write( "Let's put the two equations into the slope-intercept form: y = mx+b<BR>\n" );
document.write( "First equation:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=px%2B4y-2+=+0 ALIGN=MIDDLE  ALT=\"px%2B4y-2+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract px from both sides of the equation.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4y-2+=+-px ALIGN=MIDDLE  ALT=\"4y-2+=+-px\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add 2 to both sides.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4y+=+-px%2B2 ALIGN=MIDDLE  ALT=\"4y+=+-px%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Finally, divide both sides by 4.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%28-p%2F4%29x%2B2%2F4 ALIGN=MIDDLE  ALT=\"y+=+%28-p%2F4%29x%2B2%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%28-p%2F4%29x%2B1%2F2 ALIGN=MIDDLE  ALT=\"y+=+%28-p%2F4%29x%2B1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Here, the slope is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m+=+%28-p%2F4%29 ALIGN=MIDDLE  ALT=\"m+=+%28-p%2F4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Second equation:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x-y%2Bp+=+0 ALIGN=MIDDLE  ALT=\"2x-y%2Bp+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add y to both sides.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%2Bp+=+y ALIGN=MIDDLE  ALT=\"2x%2Bp+=+y\"   DISABLED_style= \"max-width:90%; height:auto;\" > or<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+2x%2Bp ALIGN=MIDDLE  ALT=\"y+=+2x%2Bp\"   DISABLED_style= \"max-width:90%; height:auto;\" > Here, the slope is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m+=+2 ALIGN=MIDDLE  ALT=\"m+=+2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The negative reciprocal of 2 is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%2F2%29 ALIGN=MIDDLE  ALT=\"-1%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and this should equal the slope of the first equation, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-p%2F4%29 ALIGN=MIDDLE  ALT=\"%28-p%2F4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so...<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-p%2F4%29+=+-1%2F2 ALIGN=MIDDLE  ALT=\"%28-p%2F4%29+=+-1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify and solve for p. Multiply both sides by -4.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p+=+4%2F2 ALIGN=MIDDLE  ALT=\"p+=+4%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p+=+2 ALIGN=MIDDLE  ALT=\"p+=+2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Check, are the slopes negative reciprocals?<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m+=+%28-p%2F4%29 ALIGN=MIDDLE  ALT=\"m+=+%28-p%2F4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Substitute p = 2.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m+=+%28-2%2F4%29 ALIGN=MIDDLE  ALT=\"m+=+%28-2%2F4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m+=+-1%2F2 ALIGN=MIDDLE  ALT=\"m+=+-1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > ...and this is the negative reciprocal of 2.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );