document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=945144>Question 945144</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Are the graphs of the lines in the pair parallel? Explain.\r<BR>\n" );
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document.write( "y = 3x + 10\r<BR>\n" );
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document.write( "12x – 3y = –36 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #576316 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=576316\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> to determine if the graphs of the lines in the pair are parallel or not, all we need is to find slopes and if both <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=slopes ALIGN=MIDDLE  ALT=\"slopes\"   DISABLED_style= \"max-width:90%; height:auto;\" > are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=equal ALIGN=MIDDLE  ALT=\"equal\"   DISABLED_style= \"max-width:90%; height:auto;\" >, lines <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=are ALIGN=MIDDLE  ALT=\"are\"   DISABLED_style= \"max-width:90%; height:auto;\" > parallel\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+highlight%283%29x+%2B+10 ALIGN=MIDDLE  ALT=\"y+=+highlight%283%29x+%2B+10\"   DISABLED_style= \"max-width:90%; height:auto;\" >...this line is already in slope-intercept form and we see that slope is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   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=12x+-3y+=-36 ALIGN=MIDDLE  ALT=\"12x+-3y+=-36\"   DISABLED_style= \"max-width:90%; height:auto;\" >..this line need to be written in slope-intercept form first\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12x+%2B36+=3y ALIGN=MIDDLE  ALT=\"12x+%2B36+=3y\"   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=12x%2F3+%2B36%2F3+=3y%2F3 ALIGN=MIDDLE  ALT=\"12x%2F3+%2B36%2F3+=3y%2F3\"   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=y=highlight%284%29x+%2B12+ ALIGN=MIDDLE  ALT=\"y=highlight%284%29x+%2B12+\"   DISABLED_style= \"max-width:90%; height:auto;\" > ...as you can see, the slope of this line is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4 ALIGN=MIDDLE  ALT=\"4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "since these lines have different slopes, we know they are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=NOT ALIGN=MIDDLE  ALT=\"NOT\"   DISABLED_style= \"max-width:90%; height:auto;\" > <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=parallel ALIGN=MIDDLE  ALT=\"parallel\"   DISABLED_style= \"max-width:90%; height:auto;\" >; they intersect in one point\r<BR>\n" );
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document.write( "see it on a graph:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+4x+%2B12%2C+3x+%2B+10%29+ ALIGN=MIDDLE  ALT=\"+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+4x+%2B12%2C+3x+%2B+10%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "  </SPAN>\n" );
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