document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=261485>Question 261485</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The equation of the line tangent to the curve y=kx+8/k+x at x=-2 is y=x+4. What is the value of k?\r<BR>\n" );
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document.write( "(A) -3<BR>\n" );
document.write( "(B) -1<BR>\n" );
document.write( "(C) 1<BR>\n" );
document.write( "(D) 3<BR>\n" );
document.write( "(E) 4 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #192669 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=192669\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Because the curve <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28kx%2B8%29%2F%28k%2Bx%29 ALIGN=MIDDLE  ALT=\"y=%28kx%2B8%29%2F%28k%2Bx%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > has a tangent line of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=x%2B4 ALIGN=MIDDLE  ALT=\"y=x%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" > at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-2 ALIGN=MIDDLE  ALT=\"x=-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, this means that the curve intersects the line at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-2 ALIGN=MIDDLE  ALT=\"x=-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and they intersect at the same 'y' value. In other words, the curve and the line intersect at the point (-2, y). Because these y values are the same, we can plug <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=x%2B4 ALIGN=MIDDLE  ALT=\"y=x%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" > into <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28kx%2B8%29%2F%28k%2Bx%29 ALIGN=MIDDLE  ALT=\"y=%28kx%2B8%29%2F%28k%2Bx%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B4=%28kx%2B8%29%2F%28k%2Bx%29 ALIGN=MIDDLE  ALT=\"x%2B4=%28kx%2B8%29%2F%28k%2Bx%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. \r<BR>\n" );
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document.write( "Now plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-2 ALIGN=MIDDLE  ALT=\"x=-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > (since they intersect at x=-2) to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2%2B4=%28-2k%2B8%29%2F%28k-2%29 ALIGN=MIDDLE  ALT=\"-2%2B4=%28-2k%2B8%29%2F%28k-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and simplify to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2=%28-2k%2B8%29%2F%28k-2%29 ALIGN=MIDDLE  ALT=\"2=%28-2k%2B8%29%2F%28k-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. From here, it's just a simple matter of solving for k which I'll let you do. </SPAN>\n" );
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