document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=202793>Question 202793</A>: <I><SPAN STYLE=\"word-break: break-all;\"> find the equation of the tangent line to the curve y=9e^-7x at the point (0,9)<BR>\n" );
document.write( "y(x)=\r<BR>\n" );
document.write( "\n" );
document.write( "can someone help please<BR>\n" );
document.write( "thanks </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #152959 by </B><A HREF=/tutors/aboutme.mpl?userid=jsmallt9><B>jsmallt9(3758)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jsmallt9><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=152959\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The simplest way to solve this is with Calculus. If you are not in a Calculus (or pre Calculus) class, then you might want to repost this so you can get a different solution.<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+9e%5E%28-7x%29 ALIGN=MIDDLE  ALT=\"y+=+9e%5E%28-7x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28dy%29%2F%28dx%29+=+%28-7%29%2A9e%5E%28-7x%29+=+-63e%5E%28-7x%29 ALIGN=MIDDLE  ALT=\"%28dy%29%2F%28dx%29+=+%28-7%29%2A9e%5E%28-7x%29+=+-63e%5E%28-7x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "To find the slope of the tangent at the point (0, 9) we substitute the x-coordinate into dy/dx:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m+=+-63e%5E%28-7%280%29%29+=+-63e%5E0+=+-63%2A1+=+-63 ALIGN=MIDDLE  ALT=\"m+=+-63e%5E%28-7%280%29%29+=+-63e%5E0+=+-63%2A1+=+-63\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now we have the slope: -63. And with a point, (0,9) we can return to first-year Algebra to find the equation of the tangent line. Using the Point-slope form: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+-+y%5B1%5D+=+m%28x+-+x%5B1%5D%29 ALIGN=MIDDLE  ALT=\"y+-+y%5B1%5D+=+m%28x+-+x%5B1%5D%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and substituting -63 for m and (0, 9) for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5B1%5D+ ALIGN=MIDDLE  ALT=\"+x%5B1%5D+\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y%5B1%5D+ ALIGN=MIDDLE  ALT=\"+y%5B1%5D+\"   DISABLED_style= \"max-width:90%; height:auto;\" > respectively we get:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+-+9+=+-63%28x+-+0%29 ALIGN=MIDDLE  ALT=\"y+-+9+=+-63%28x+-+0%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "This may be an acceptable answer. But often equations of lines are expected in slope-intercept form: y = mx + b. So we will transform the above into slope-intercept form. First we simplify:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+-+9+=+-63%28x%29+=+-63x ALIGN=MIDDLE  ALT=\"y+-+9+=+-63%28x%29+=+-63x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Adding 9 to both sides:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+-63x+%2B+9 ALIGN=MIDDLE  ALT=\"y+=+-63x+%2B+9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "And now we have the equation of the requested tangent line, in slope-intercept form. </SPAN>\n" );
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