document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=984646>Question 984646</A>: <I><SPAN STYLE=\"word-break: break-all;\"> the two lines a1x+b1y+c1=0 and a2x+b2y+c2=0 are identical if </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #605423 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=605423\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the equations are multiples of each other.\r<BR>\n" );
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document.write( "an example:\r<BR>\n" );
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document.write( "x + y + 3 = 0<BR>\n" );
document.write( "2x + 2y + 6 = 0\r<BR>\n" );
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document.write( "these equations are multiples of each other.\r<BR>\n" );
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document.write( "convert each equation to slope intercept form of y = mx + b.<BR>\n" );
document.write( "m is the slope.<BR>\n" );
document.write( "b is the y-intercept.\r<BR>\n" );
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document.write( "start with x + y + 3 = 0<BR>\n" );
document.write( "subtract x from both sides and subtract 3 from both sides to get:<BR>\n" );
document.write( "y = -x - 3\r<BR>\n" );
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document.write( "start with 2x + 2y + 6 = 0<BR>\n" );
document.write( "subtract 2x from both sides and subtract 6 from both sides to get:<BR>\n" );
document.write( "2y = -2x - 6<BR>\n" );
document.write( "divide both sides by 2 to get:<BR>\n" );
document.write( "y = -x - 3\r<BR>\n" );
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document.write( "in slope intercept form the two equations are identical.<BR>\n" );
document.write( "first equation is:<BR>\n" );
document.write( "y = -x - 3<BR>\n" );
document.write( "second equation is:<BR>\n" );
document.write( "y = -x - 3\r<BR>\n" );
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document.write( "the slope intercept form of the equation is y = mx + b where m is the slope and b is the y-intercept.\r<BR>\n" );
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document.write( "both equations have the same slope (-1) so they are either parallel or identical.\r<BR>\n" );
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document.write( "both equation have the same y-intercept so they are identical.\r<BR>\n" );
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document.write( "equations are identical if they have the same slope and the same y-intercept.\r<BR>\n" );
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document.write( "equations are parallel if they have the same slope and different y-intercepts.\r<BR>\n" );
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document.write( "those are the rules.<BR>\n" );
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