document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=198174>Question 198174</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I tried to figure out this problem and do not really know how to do it.\r<BR>\n" );
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document.write( "Write a function rule for the table:\r<BR>\n" );
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document.write( "x   f(x)<BR>\n" );
document.write( "2   -8<BR>\n" );
document.write( "3   -12<BR>\n" );
document.write( "4   -16<BR>\n" );
document.write( "5   -20\r<BR>\n" );
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document.write( "I think the answer is f(x)=-4x+-8 but I am not sure.<BR>\n" );
document.write( "Thank You! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #148653 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=148653\">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( "Let's check your work:\r<BR>\n" );
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document.write( "You say:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ f(x) = -4x - 8\">.\r<BR>\n" );
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document.write( "That means if we substitute any pair of values from your table for <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE x\"> and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large f(x)\">, then we should have a true statement.  Let's try it:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ -8 =^? -4(2) - 8 = -8 -8 = -16\">.\r<BR>\n" );
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document.write( "Oops!  First one fails. So we can guarantee that your function is not the one we are looking for.  Back to the drawing board -- literally.\r<BR>\n" );
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document.write( "First thing to do is to create four ordered pairs from the pairs of numbers in your table.  (2, -8), (3, -12), and so on.  Then plot these points on a graph (see I told you we were going back to the drawing board).  If you plot them correctly, you will see that they all lie in one straight line.\r<BR>\n" );
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document.write( "Since the points all lie in a straight line, we know that we have a linear function.  All you need to do now is pick two of the pairs and use the two-point form of the equation of a line to develop your function:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ f(x) - y_1 = \left(\frac{y_1 - y_2}{x_1 - x_2}\right)(x - x_1) \">\r<BR>\n" );
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document.write( "Substitute the coordinates from any two of the points and then do the arithmetic and solve for <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large f(x)\">\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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