document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=30514>Question 30514</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I need help with a linear function table.  Here's the table:\r<BR>\n" );
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document.write( "x       f(x)<BR>\n" );
document.write( "-6      -15<BR>\n" );
document.write( "1        -1<BR>\n" );
document.write( "7       11<BR>\n" );
document.write( "11      19\r<BR>\n" );
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document.write( "I tried to find the pattern for the y's and the x's so that I could find the slope, but it doesn't seem like there is a pattern.  I need to write the rule for the linear equation.  Can you help?\r<BR>\n" );
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document.write( "Thanks </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #17182 by </B><A HREF=/tutors/aboutme.mpl?userid=longjonsilver><B>longjonsilver(2297)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=longjonsilver><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=longjonsilver><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=17182\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> you say it is a linear function, so in that case, we are looking for a \"times table\".\r<BR>\n" );
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document.write( "Pick any 2 values of x... say 7 and 11. They differ by 4. Their F(x) values are 11 and 19, which differ by 8.\r<BR>\n" );
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document.write( "So, x increases by 4 whilst y increases by 8... looks like the 2 times table to me.\r<BR>\n" );
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document.write( "--> f(x) = 2x\r<BR>\n" );
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document.write( "Now, it isn't THE 2x table: 2,4,6,8,10,... etc, but it is this shifted.\r<BR>\n" );
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document.write( "So, when x=7, f(x)=2x gives f(x)=14. Our function actually gives 11, so we need to subtract 3: f(x)= 2x-3.\r<BR>\n" );
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document.write( "CHECK:<BR>\n" );
document.write( "when x=-6<BR>\n" );
document.write( "f(-6) = 2(-6) - 3<BR>\n" );
document.write( "f(-6) = -12 - 3<BR>\n" );
document.write( "f(-6) = -15... CORRECT\r<BR>\n" );
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document.write( "You can then tell what the slope of the line is from y=2x-3\r<BR>\n" );
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document.write( "jon. </SPAN>\n" );
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