document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=503419>Question 503419</A>: <I><SPAN STYLE=\"word-break: break-all;\"> What is the slope of this tangent if given this point?\r<BR>\n" );
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document.write( "y=4/x (-2,8)\r<BR>\n" );
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document.write( "It reads: y equals four over x<BR>\n" );
document.write( "The given point is: (-2, 8)\r<BR>\n" );
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document.write( "An explanation as to how the answer was reached would be wonderful! :) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #339229 by </B><A HREF=/tutors/aboutme.mpl?userid=oberobic><B>oberobic(2304)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=oberobic><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=339229\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Looking at the graph, you can see that y = 4/x is not truly a linear equation.<BR>\n" );
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document.write( "Actually<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+4+%2A+x%5E%28-1%29 ALIGN=MIDDLE  ALT=\"y+=+4+%2A+x%5E%28-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "The point (-2,8) is not on the curve, which you see above.  Or prove it by plugging the x value into the equation:<BR>\n" );
document.write( "y = 4/x<BR>\n" );
document.write( "x = -2<BR>\n" );
document.write( "y = -2, not 8\r<BR>\n" );
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document.write( "That creates another problem for you.<BR>\n" );
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document.write( "In general the slope of a line tangent to a curve can be found using the first derivative.<BR>\n" );
document.write( "But that is a calculus question, not algebra.<BR>\n" );
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document.write( "The first derivative of <BR>\n" );
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document.write( "That is the slope of the line tangent to the curve for any value of 'x'.<BR>\n" );
document.write( "But you need a point on the curve, which you do not have.<BR>\n" );
document.write( "So, there is something wrong with your problem statement.<BR>\n" );
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document.write( "But assuming the point = (-2,-2)<BR>\n" );
document.write( "The slope is:<BR>\n" );
document.write( "-4/(-2^2) = -4/4 = -1 at that point.<BR>\n" );
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document.write( "Remember this is a curve, so the slope changes continuously.<BR>\n" );
document.write( "(except there is a discontinuity at x=0 because 4/0 is undefined)<BR>\n" );
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document.write( "Substituting in the slope-intercept equation:<BR>\n" );
document.write( "y = mx+b\r<BR>\n" );
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document.write( "-2 = -1*(-2) + b<BR>\n" );
document.write( "b = -4<BR>\n" );
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document.write( "y = -x -4<BR>\n" );
document.write( "which is a linear equation.<BR>\n" );
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document.write( "Of course, you could have picked another point.<BR>\n" );
document.write( "Let's say x =4<BR>\n" );
document.write( "The curve is y = x/4, so y=1.<BR>\n" );
document.write( "(4,1)<BR>\n" );
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document.write( "m = -4/(4^2) = -4/16 = -1/4<BR>\n" );
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document.write( "1 = -1/4(4) + b<BR>\n" );
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document.write( "so<BR>\n" );
document.write( "b=2<BR>\n" );
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document.write( "y = (-1/4)x+2<BR>\n" );
document.write( "which is a linear equation tangent to the curve at (4,1)\r<BR>\n" );
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document.write( " </SPAN>\n" );
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