document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1065873>Question 1065873</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Determine the point <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28x%2C+y%29+ ALIGN=MIDDLE  ALT=\"P%28x%2C+y%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > on the graph of the equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=+sqrt+%28x%2B1%29+ ALIGN=MIDDLE  ALT=\"y=+sqrt+%28x%2B1%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > such that the slope of the line through the point (3, 2) and P is 3/8 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #681053 by </B><A HREF=/tutors/aboutme.mpl?userid=Boreal><B>Boreal(15235)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Boreal><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=Boreal><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=681053\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C300%2C-10%2C10%2C-10%2C10%2Csqrt%28x%2B1%29%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C300%2C-10%2C10%2C-10%2C10%2Csqrt%28x%2B1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The point is (x,y). The slope is (2-y)/(3-x)=(3/8)<BR>\n" );
document.write( "That is 16-8y=9-3x<BR>\n" );
document.write( "or 3x+7=8y; but y = sqrt (x+1)<BR>\n" );
document.write( "right side is 8 sqrt (x+1)<BR>\n" );
document.write( "square both sides<BR>\n" );
document.write( "9x^2+42x+49=64(x+1)=64x+64<BR>\n" );
document.write( "9x^2-22x-15=0<BR>\n" );
document.write( "(9x+5)(x-3)=0<BR>\n" );
document.write( "x=3 (doesn't help) and x=-5/9<BR>\n" );
document.write( "y is sqrt ( -5/9 +1)= sqrt (4/9) =2/3<BR>\n" );
document.write( "the slope between (-5/9,2/3) and (3,2)=2-(2/3) or 12/9 divided by 3-(-5/9)=32/9<BR>\n" );
document.write( "12/9 divided by 32/9 is 3/8.<BR>\n" );
document.write( "The point has to be to the left of (3,2), because the derivative is 1/2 sqrt (x+1), which at x=3 gives a slope of 1/(2*2)=1/4, and the slope gets less further to the right. </SPAN>\n" );
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