document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=249105>Question 249105</A>: <I><SPAN STYLE=\"word-break: break-all;\"> are the graph of the lines in the pair parallel?explain\r<BR>\n" );
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document.write( "y=5x+6\r<BR>\n" );
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document.write( "-18+3y=-54 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #181541 by </B><A HREF=/tutors/aboutme.mpl?userid=College+Student><B>College Student(505)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=College+Student><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=College+Student><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=181541\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Are the graph of the lines in the pair parallel?  Explain.\r<BR>\n" );
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document.write( "y=5x+6   ...and...   -18+3y=-54\r<BR>\n" );
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document.write( "Facts:  <BR>\n" );
document.write( "1.  Two parallel lines share the same slope.<BR>\n" );
document.write( "2.  To determine a slope, express the equations in this 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;\" ><BR>\n" );
document.write( "3.  m = slope\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=5x%2B6 ALIGN=MIDDLE  ALT=\"y=5x%2B6\"   DISABLED_style= \"max-width:90%; height:auto;\" >  <--- already in y=mx+b form\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-18%2B3y=-54 ALIGN=MIDDLE  ALT=\"-18%2B3y=-54\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3y=-54%2B18 ALIGN=MIDDLE  ALT=\"3y=-54%2B18\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3y=-36 ALIGN=MIDDLE  ALT=\"3y=-36\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-36%2F3 ALIGN=MIDDLE  ALT=\"y=-36%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-12 ALIGN=MIDDLE  ALT=\"y=-12\"   DISABLED_style= \"max-width:90%; height:auto;\" >  <--- there is no x value, thus we cannot express it in y=mx+b form\r<BR>\n" );
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document.write( "The answer is: they are not parallel because they do not share the same slope.\r<BR>\n" );
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document.write( "Here is how the graph of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=5x%2B6 ALIGN=MIDDLE  ALT=\"y=5x%2B6\"   DISABLED_style= \"max-width:90%; height:auto;\" > looks like:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph+%28300%2C+300%2C+-7%2C+7%2C+-7%2C+7%2C+5x%2B6%29 ALIGN=MIDDLE  ALT=\"graph+%28300%2C+300%2C+-7%2C+7%2C+-7%2C+7%2C+5x%2B6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The slope of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-12 ALIGN=MIDDLE  ALT=\"y=-12\"   DISABLED_style= \"max-width:90%; height:auto;\" > is zero, because it represents a horizontal line in the cartesian plane.<BR>\n" );
document.write( "We know that a slope = rise/run... in this case there is no rise and the run goes to infinity (+ and - directions).  When zero is divided by any number, the result is zero... thus the slope is zero.<BR>\n" );
document.write( "Here is how the graph of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-12 ALIGN=MIDDLE  ALT=\"y=-12\"   DISABLED_style= \"max-width:90%; height:auto;\" > looks like:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph+%28300%2C+300%2C+-7%2C+7%2C+-18%2C+7%2C+-12%29 ALIGN=MIDDLE  ALT=\"graph+%28300%2C+300%2C+-7%2C+7%2C+-18%2C+7%2C+-12%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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