document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=447691>Question 447691</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I have the following points (25, 16) and (40,26) and thanks to the very generous help of scott8148 I was able to figure out the first two part of this problem.  I figured out the slope as m=2/3, and with that I figured out the y-intercept as<BR>\n" );
document.write( "- 2/3. Using this equation that he graciously provided.  This points represented the height a ball was dropped from as the x-axis and the bounce heights as the y axis.  <BR>\n" );
document.write( "So given the information above how would I set up an equation to determine the value of x if y=100.  I also know that on this same graph is the point (50,33) So would I be correct in assuming then that by increasing the the value of x to something like 151 I would thus attain a y value of approximately 100?\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #308158 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=308158\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
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document.write( "Just so that no one who reads this later gets lost, let's take it from the top:\r<BR>\n" );
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document.write( "You are looking for a linear function, <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large f(x)\"> such that if <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\ =\ 25\"> then <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large y\ =\ 16\"> -- that gives you the point (26,16).  Also if <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\ =\ 40\"> then <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large y\ =\ 26\"> -- the point (40, 26).\r<BR>\n" );
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document.write( "You did the slope calculation correctly:  <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \frac{y_2\ -\ y_1}{x_2\ -\ x_1}\ =\ \frac{26\ -\ 16}{40\ -\ 25}\ =\ \frac{10}{15}\ =\ \frac{2}{3}\">\r<BR>\n" );
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document.write( "And then, using the point-slope form of the equation of a line:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ y\ -\ y_1\ =\ m(x\ -\ x_1) \">\r<BR>\n" );
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document.write( "where <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \left(x_1,y_1\right)\"> are the coordinates of a point on the line and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large m\"> is the slope:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ y\ -\ 16\ =\ \frac{2}{3}(x\ -\ 25)\">\r<BR>\n" );
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document.write( "from which you derived:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ y\ =\ \frac{2}{3}x\ -\ \frac{2}{3}\">\r<BR>\n" );
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document.write( "And correctly discovered that the <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large y\">-intercept is <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large -\frac{2}{3}\">\r<BR>\n" );
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document.write( "But that IS your function:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ f(x)\ =\ \frac{2}{3}x\ -\ \frac{2}{3}\">\r<BR>\n" );
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document.write( "Pick any value you like for <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\">, insert that value in place of <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\">, and do the arithmetic.\r<BR>\n" );
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document.write( "Let's check it out:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{2}{3}(25)\ -\ \frac{2}{3}\ =\ \frac{48}{3}\ =\ 16\">\r<BR>\n" );
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document.write( "That one checks, so:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{2}{3}(40)\ -\ \frac{2}{3}\ =\ \frac{78}{3}\ =\ 26\">\r<BR>\n" );
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document.write( "and this checks, so:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{2}{3}(50)\ -\ \frac{2}{3}\ =\ \frac{98}{3}\ =\ 32\frac{2}{3}\ \neq\ 33\">\r<BR>\n" );
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document.write( "Well, almost, so\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{2}{3}(100)\ -\ \frac{2}{3}\ =\ \frac{??}{3}\ =\ ??\">\r<BR>\n" );
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document.write( "I'll let you do the arithmetic for the last one.\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" );
document.write( "My calculator said it, I believe it, that settles it<BR>\n" );
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