document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1136952>Question 1136952</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the points on the graph y=7x/x-2 where the slope of the tangent line is parallel to the line 28x+2y-17=0 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #754781 by </B><A HREF=/tutors/aboutme.mpl?userid=rothauserc><B>rothauserc(4718)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rothauserc><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=rothauserc><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=754781\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I assume you mean the following equation, always use parenthesis to clarify intent<BR>\n" );
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document.write( "y = 7x/(x-2)<BR>\n" );
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document.write( "use the quotient rule to find the first derivative<BR>\n" );
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document.write( "let u be 7x and v be x-2<BR>\n" );
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document.write( "y' = 7 * ( (x-2)*1 - x(1) ) / (x-2)^2 = -14/(x-2)^2<BR>\n" );
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document.write( "find slope of the given line by rewriting it as slope intercept form<BR>\n" );
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document.write( "28x +2y -17 = 0<BR>\n" );
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document.write( "2y = -28x +17<BR>\n" );
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document.write( "y = -14x +17/2<BR>\n" );
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document.write( "slope is -14, set first derivative equal to -14<BR>\n" );
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document.write( "-14/(x-2)^2 = -14/1<BR>\n" );
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document.write( "cross multiply fractions<BR>\n" );
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document.write( "-14(x-2)^2 = -14<BR>\n" );
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document.write( "(x-2)^2 = 1<BR>\n" );
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document.write( "x-2 = + or - 1<BR>\n" );
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document.write( "x = 2 +1 = 3<BR>\n" );
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document.write( "x = 2 -1 = 1<BR>\n" );
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document.write( "we have two points whose x-coordinate is 3 or 1, we use the original equation to find the corresponding y coordinates<BR>\n" );
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document.write( "f(3) = 7(3)/(3-2) = 21<BR>\n" );
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document.write( "f(1) = 7(1)/(1-2) = -7<BR>\n" );
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document.write( "the two points are (3,21) and (1,-7)<BR>\n" );
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