document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=888907>Question 888907</A>: <I><SPAN STYLE=\"word-break: break-all;\"> pls help me to answer with solution ; what is the value of k so that the line x+(3k-2)y+10=0 and is parallel to the line x+5y+2=0<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #537746 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=537746\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> you want to to convert both equation into slope intercept form.\r<BR>\n" );
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document.write( "slope intercept form is y = mx + b\r<BR>\n" );
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document.write( "once in this form:\r<BR>\n" );
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document.write( "m = slope<BR>\n" );
document.write( "b = y-intercept.\r<BR>\n" );
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document.write( "if the slope of both equation is the same and the y-intercept is different, then the lines are parallel.\r<BR>\n" );
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document.write( "start with x + 5y + 2 = 0<BR>\n" );
document.write( "subtract x and subtract 2 from both sides of the equation to get:<BR>\n" );
document.write( "5y = -x - 2<BR>\n" );
document.write( "divide both sides of the equation by 5 to get:<BR>\n" );
document.write( "y = -(1/5)*x - (2/5)\r<BR>\n" );
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document.write( "that's your first equation in slope intercept form.<BR>\n" );
document.write( "the slope is -(1/5).\r<BR>\n" );
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document.write( "-(1/5) is the slope you want to get in your second equation in order to make the lines parallel to each other.\r<BR>\n" );
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document.write( "start with your second equation of x + (3k-2)y + 10 = 0<BR>\n" );
document.write( "subtract 10 and subtract x from both sides of the equation to get:<BR>\n" );
document.write( "(3k-2)y = -x - 10<BR>\n" );
document.write( "divide both sides of the equation by (3k-2) to get:<BR>\n" );
document.write( "y = -(1/(3k-2)*x - (10/(3k-2))\r<BR>\n" );
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document.write( "that's your second equation in slope intercept form.<BR>\n" );
document.write( "the slope is -(1/(3k-2))\r<BR>\n" );
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document.write( "in order for the lines to be parallel, -(1/(3k-2)) must be equal to -(1/5).\r<BR>\n" );
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document.write( "set these two expressions equal to each other and solve for k.\r<BR>\n" );
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document.write( "-1/(3k-2) = -1/5\r<BR>\n" );
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document.write( "cross multiply to get:\r<BR>\n" );
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document.write( "-1*5 = -1*(3k-2)\r<BR>\n" );
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document.write( "divide both sides of this equation by (-1) to get:\r<BR>\n" );
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document.write( "5 = 3k-2\r<BR>\n" );
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document.write( "add 2 to both sides of this equation to get:\r<BR>\n" );
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document.write( "7 = 3k\r<BR>\n" );
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document.write( "divide both sides of this equation by 3 to get:\r<BR>\n" );
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document.write( "7/3 = k\r<BR>\n" );
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document.write( "that's your answer.\r<BR>\n" );
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document.write( "in order for the lines to be parallel, k has to be equal to 7/3.\r<BR>\n" );
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document.write( "to confirm, replace k with 7/3 in your original equation.\r<BR>\n" );
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document.write( "your original equation is x + (3k-2)y + 10 = 0<BR>\n" );
document.write( "replace k with 7/3 to get:<BR>\n" );
document.write( "x + (3*7/3-2)y + 10 = 0<BR>\n" );
document.write( "simplify to get:<BR>\n" );
document.write( "x + 5y + 10 = 0<BR>\n" );
document.write( "subtract x and subtract 10 from both sides of the equation to get:<BR>\n" );
document.write( "5y = -x - 10<BR>\n" );
document.write( "divide both sides of the equation by 5 to get:<BR>\n" );
document.write( "y = -(1/5)*x - (10/5)<BR>\n" );
document.write( "simplify to get:<BR>\n" );
document.write( "y = -(1/5)*x - 2\r<BR>\n" );
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document.write( "your first equation in slope intercept form is y = -(1/5)*x - (2/5)\r<BR>\n" );
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document.write( "your second equation in slope intercept form is y = -(1/5)*x - 2\r<BR>\n" );
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document.write( "the slopes are the same and the y-intercepts are different so the lines are parallel.\r<BR>\n" );
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document.write( "here's a graph of your two lines.<BR>\n" );
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