document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=133953>Question 133953</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How can you determine if two lines are perpendicular? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #97946 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=97946\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If you are given the equations of the lines, solve the equations for y in terms of x -- in other words put them into slope-intercept form, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=mx%2Bb ALIGN=MIDDLE  ALT=\"y=mx%2Bb\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  Then compare the slopes of the two lines.  Two lines are perpendicular if and only if their slopes are negative reciprocals of each other.  That is to say if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m%5B1%5D ALIGN=MIDDLE  ALT=\"m%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the slope of one of the lines and <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;\" > is the slope of the other line, the lines are perpendicular if and only if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m%5B1%5D=-%281%2Fm%5B2%5D%29 ALIGN=MIDDLE  ALT=\"m%5B1%5D=-%281%2Fm%5B2%5D%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. </SPAN>\n" );
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