document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=264700>Question 264700</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the equation of the linear function g whose graph is perpendicular to the line 2x – 9y = –45; the two lines intersect at x = 18.\r<BR>\n" );
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document.write( "The answer that I keep coming up with is y=-9/2x+81.  This is an online problem that I need to submit and it keeps telling me that I'm incorrect!  The only thing that I can think that I may be doing wrong is that I'm using the point (18,0) because that's where the lines intersect.  What am I doing wrong??? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #194823 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=194823\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Garamond\" size=\"+2\">\r<BR>\n" );
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document.write( "You are very close.\r<BR>\n" );
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document.write( "You started correctly by determining that the slope of the given line is <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \frac{2}{9}\">, therefore the slope of the perpendicular must be <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large -\frac{9}{2}\">.  But where you went astray is when you assumed that the point of intersection of the two lines is (18,0) just because it was given that the two lines intersect at <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\ =\ 18\">.\r<BR>\n" );
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document.write( "If the two lines intersect at some point where <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\ =\ 18\">, then that point must be <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \left(18,\,y\\right)\"> such that the values 18 and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large y\"> make your original given equation (and the equation we are about to derive for that matter) a true statement.  Hence:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 2\left(18\right)\ -\ 9y\ =\ -45\">\r<BR>\n" );
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document.write( "And solve for <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large y\">\r<BR>\n" );
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document.write( "I get <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large y\ =\ 9\">.  (Verification left as an exercise for the student)\r<BR>\n" );
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document.write( "And that tells us that the actual point of intersection is (18,9).  Now that we know that and the fact that the line you want to derive has a slope of  <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large -\frac{9}{2}\">, we can write:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ y\ =\ -\frac{9}{2}\left(x\right)\ +\ b\">\r<BR>\n" );
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document.write( "And then substitute the coordinate values from the point of intersection:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 9\ =\ -\frac{9}{2}\left(18\right)\ +\ b\">\r<BR>\n" );
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document.write( "Finally, solve for <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large b\"> which can then be substituted to create your final derived equation.  I get <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large b\ =\ 90\">, but you should check it for yourself.\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi} + 1 = 0\"><BR>\n" );
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