document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=274198>Question 274198</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find an equation of a linear function o(x)for which o(3)=7 and o(-1)=5.<BR>\n" );
document.write( "Then find o(20).*<BR>\n" );
document.write( "*By the way...the \"o\" is supposed to be the symbol in my problem which is an o with a vertical line through it...I'm assuming it's just a variable like x or y.<BR>\n" );
document.write( "Thanks so much for your help! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #200154 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=200154\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Garamond\" size=\"+2\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Not \"a variable like <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\"> or <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large y\">\"  This is function notation, like <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large f(x)\">.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "You want to define <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \phi(x)\"> such that <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \phi(3)\ =\ 7\"> and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \phi(-1)\ =\ 5\">.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "This is almost exactly the same thing as saying \"What is an equation, in slope-intercept form, of the line that passes through the points (3, 7) and (-1, 5)?\"\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The only difference being that in one case you would derive an equation of the form <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large y\ =\ mx\ +\ b\"> but in the given case we will derive an equation of the form <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \phi(x)\ =\ mx\ +\ b\">.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Use the two point form of the equation of a line:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ y\ -\ y_1\ =\ \left(\frac{y_1\ -\ y_2}{x_1\ -\ x_2}\right)(x\ -\ x_1) \">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Where <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \left(x_1,y_1\right)\"> and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \left(x_2,y_2\right)\"> are the coordinates of the given points.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ y\ -\ 7\ =\ \left(\frac{7\ -\ 5}{3\ -\ (-1)}\right)(x\ -\ 3)\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "A little arithmetic:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ y\ -\ 7\ =\ \left(\frac{1}{2}\right)(x\ -\ 3)\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Distributing and collecting terms:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ y\ =\ \frac{1}{2}x\ -\ \frac{3}{2}\ +\ 7\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ y\ =\ \frac{1}{2}x\ +\ \frac{11}{2}\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "And finally, replace <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large y\"> with <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \phi(x)\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \phi(x)\ =\ \frac{1}{2}x\ +\ \frac{11}{2}\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
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( "</font> </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );