document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=154332>Question 154332</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Determine whether the lines of the graph are perpendicular.<BR>\n" );
document.write( "6x-7y=5<BR>\n" );
document.write( "6y-7x=5 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #113634 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=113634\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6x-7y=5 ALIGN=MIDDLE  ALT=\"6x-7y=5\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given equation.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-7y=5-6x ALIGN=MIDDLE  ALT=\"-7y=5-6x\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6x ALIGN=MIDDLE  ALT=\"6x\"   DISABLED_style= \"max-width:90%; height:auto;\" > from both sides.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-7y=-6x%2B5 ALIGN=MIDDLE  ALT=\"-7y=-6x%2B5\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rearrange the terms.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28-6x%2B5%29%2F%28-7%29 ALIGN=MIDDLE  ALT=\"y=%28-6x%2B5%29%2F%28-7%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-7 ALIGN=MIDDLE  ALT=\"-7\"   DISABLED_style= \"max-width:90%; height:auto;\" > to isolate y.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28%28-6%29%2F%28-7%29%29x%2B%285%29%2F%28-7%29 ALIGN=MIDDLE  ALT=\"y=%28%28-6%29%2F%28-7%29%29x%2B%285%29%2F%28-7%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Break up the fraction.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%286%2F7%29x-5%2F7 ALIGN=MIDDLE  ALT=\"y=%286%2F7%29x-5%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" > Reduce.\r<BR>\n" );
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document.write( "So we can see that the equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%286%2F7%29x-5%2F7 ALIGN=MIDDLE  ALT=\"y=%286%2F7%29x-5%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" > has a slope <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=6%2F7 ALIGN=MIDDLE  ALT=\"m=6%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" > and a y-intercept <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=-5%2F7 ALIGN=MIDDLE  ALT=\"b=-5%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6y-7x=5 ALIGN=MIDDLE  ALT=\"6y-7x=5\"   DISABLED_style= \"max-width:90%; height:auto;\" > Now move onto the second equation.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6y=57x ALIGN=MIDDLE  ALT=\"6y=57x\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7x ALIGN=MIDDLE  ALT=\"7x\"   DISABLED_style= \"max-width:90%; height:auto;\" > to both sides.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6y=7x%2B5 ALIGN=MIDDLE  ALT=\"6y=7x%2B5\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rearrange the terms.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%287x%2B5%29%2F%286%29 ALIGN=MIDDLE  ALT=\"y=%287x%2B5%29%2F%286%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6 ALIGN=MIDDLE  ALT=\"6\"   DISABLED_style= \"max-width:90%; height:auto;\" > to isolate y.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28%287%29%2F%286%29%29x%2B%285%29%2F%286%29 ALIGN=MIDDLE  ALT=\"y=%28%287%29%2F%286%29%29x%2B%285%29%2F%286%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Break up the fraction.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%287%2F6%29x%2B5%2F6 ALIGN=MIDDLE  ALT=\"y=%287%2F6%29x%2B5%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" > Reduce.\r<BR>\n" );
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document.write( "So we can see that the equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%287%2F6%29x%2B5%2F6 ALIGN=MIDDLE  ALT=\"y=%287%2F6%29x%2B5%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" > has a slope <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=7%2F6 ALIGN=MIDDLE  ALT=\"m=7%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" > and a y-intercept <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=5%2F6 ALIGN=MIDDLE  ALT=\"b=5%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "So the slope of the first line is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=6%2F7 ALIGN=MIDDLE  ALT=\"m=6%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" > and the slope of the second line is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=7%2F6 ALIGN=MIDDLE  ALT=\"m=7%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Since the two slopes are neither equal nor negative reciprocals of one another, the two lines are neither parallel nor perpendicular.\r<BR>\n" );
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