document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=587243>Question 587243</A>: <I><SPAN STYLE=\"word-break: break-all;\"> What is the slope of the line tangent to the curve 3y^2-2x^2=6-2xy at the point (3,2)? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #374039 by </B><A HREF=/tutors/aboutme.mpl?userid=Alan3354><B>Alan3354(69443)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Alan3354><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=Alan3354><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=374039\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> What is the slope of the line tangent to the curve 3y^2-2x^2=6-2xy at the point (3,2)?<BR>\n" );
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document.write( "3y^2-2x^2=6-2xy<BR>\n" );
document.write( "6ydy - 4xdx = -2(xdy + ydx) = -2xdy - 2ydx<BR>\n" );
document.write( "6ydy + 2ydy = -2ydx + 4xdx<BR>\n" );
document.write( "4ydy = (2x - y)dx<BR>\n" );
document.write( "dy/dx = (2x - y)/4y<BR>\n" );
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document.write( "f'(3,2) = (6 - 2)/(4*2) = 1/2<BR>\n" );
document.write( "Tangent line:  2y = x + 1\r<BR>\n" );
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