document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=252793>Question 252793</A>: <I><SPAN STYLE=\"word-break: break-all;\"> What is the value of k if the line 3x - 2y  =  1 is parallel to the line y - (2k + 1)x  = 3? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #184855 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=184855\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> convert both equations to slope intercept form.\r<BR>\n" );
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document.write( "slope intercept form of linear 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( "3x - 2y = 1 is the first equation.<BR>\n" );
document.write( "subtract 3x from both sides to get:<BR>\n" );
document.write( "-2y = -3x + 1<BR>\n" );
document.write( "divide both sides of the equation by -2 to get:<BR>\n" );
document.write( "y = (3/2)*x - (1/2)\r<BR>\n" );
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document.write( "slope for this equation is (3/2).\r<BR>\n" );
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document.write( "y - (2k + 1)*x = 3 is the second equation.<BR>\n" );
document.write( "add (2k+1)*x to both sides to get:<BR>\n" );
document.write( "y = (2k+1)*x + 3\r<BR>\n" );
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document.write( "slope for this equation is (2k+1)\r<BR>\n" );
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document.write( "if the lines are parallel, then their slopes are equal.\r<BR>\n" );
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document.write( "this means that:\r<BR>\n" );
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document.write( "2k+1 = (3/2)\r<BR>\n" );
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document.write( "subtract 1 from both sides of this equation to get:\r<BR>\n" );
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document.write( "2k = 1/2\r<BR>\n" );
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document.write( "divide both sides of this equation by 2 to get:\r<BR>\n" );
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document.write( "k = (1/4)\r<BR>\n" );
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document.write( "your answer should be k = (1/4)\r<BR>\n" );
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document.write( "substitute this value for k in the second equation.\r<BR>\n" );
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document.write( "second equation is:\r<BR>\n" );
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document.write( "y - (2k + 1)*x = 3\r<BR>\n" );
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document.write( "substitute k = (1/4) in this equation to get:\r<BR>\n" );
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document.write( "y - (2*(1/4) + 1)*x = 3\r<BR>\n" );
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document.write( "simplify to get:\r<BR>\n" );
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document.write( "y - (3/2)*x = 3\r<BR>\n" );
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document.write( "add (3/2)*x to both sides of this equation to get:\r<BR>\n" );
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document.write( "y = (3/2)*x + 3\r<BR>\n" );
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document.write( "your two equations are:\r<BR>\n" );
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document.write( "y = (3/2)*x - (1/2) (first equation)<BR>\n" );
document.write( "y = (3/2)*x + 3 (second equation)\r<BR>\n" );
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document.write( "since they have the same slope, they are parallel to each other.\r<BR>\n" );
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document.write( "graph of these equations looks like this:\r<BR>\n" );
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document.write( " </SPAN>\n" );
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