document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=113465>Question 113465</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help, i dont understand this!<BR>\n" );
document.write( "Are the following lines parallel, perpendicular, or neither?<BR>\n" );
document.write( "   L1 with equation x – 6y = 24<BR>\n" );
document.write( "   L2 with equation 6x + y = 6<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #82540 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=82540\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Parallel lines have slopes that are equal, and perpendicular lines have slopes that are the negative reciprocal of each other <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m%5B1%5D=%28-1%29%2Fm%5B2%5D ALIGN=MIDDLE  ALT=\"m%5B1%5D=%28-1%29%2Fm%5B2%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Now the problem is to find the slope on each of the two lines and compare them.  The equations are currently in standard form, so we need to convert them to slope-intercept form.  The slope-intercept form is <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;\" > where m is the slope.  All that needs to be done is rearrange the equations so they have y on the left and everything else on the right.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-6y=24 ALIGN=MIDDLE  ALT=\"x-6y=24\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-6y=-x%2B24 ALIGN=MIDDLE  ALT=\"-6y=-x%2B24\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Add -x to both sides<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%281%2F6%29x-4 ALIGN=MIDDLE  ALT=\"y=%281%2F6%29x-4\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Divide both sides by -6\r<BR>\n" );
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document.write( "Now we know the slope of the first line is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m%5B1%5D=1%2F6 ALIGN=MIDDLE  ALT=\"m%5B1%5D=1%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Let's do the second one the same way.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6x%2By=6 ALIGN=MIDDLE  ALT=\"6x%2By=6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-6x%2B6 ALIGN=MIDDLE  ALT=\"y=-6x%2B6\"   DISABLED_style= \"max-width:90%; height:auto;\" > A -6x to both sides\r<BR>\n" );
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document.write( "Now we know the slope of the second line is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m%5B2%5D=-6 ALIGN=MIDDLE  ALT=\"m%5B2%5D=-6\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Comparing them we see that <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;\" >, therefore the lines are perpendicular.\r<BR>\n" );
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document.write( "Hope this helps,<BR>\n" );
document.write( "John </SPAN>\n" );
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