document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=295569>Question 295569</A>: <I><SPAN STYLE=\"word-break: break-all;\"> When dealing with Functional Relationships I need to know what the equation to represent each function is with the table provided.  The table is an input/output table. The input numbers are: 5, 6, 7, 8, and 9.  The output numbers are: 5, ?, 9, 11, and 13.  I know that the ? is 7, just by the pattern.  What I don't know is what equation could I write to give me that in every instance? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #213063 by </B><A HREF=/tutors/aboutme.mpl?userid=richwmiller><B>richwmiller(17219)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=richwmiller><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=richwmiller><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=213063\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let's look at the input output<BR>\n" );
document.write( "5 5 diff 0<BR>\n" );
document.write( "6 ? diff ?<BR>\n" );
document.write( "7 9 diff 2<BR>\n" );
document.write( "8 11 diff 3<BR>\n" );
document.write( "9 13 diff 4<BR>\n" );
document.write( "y=5+(x-5)*2<BR>\n" );
document.write( "let's try it<BR>\n" );
document.write( "y=5+(5-5)*2=5+0=5<BR>\n" );
document.write( "y=5+(6-5)*2=5+2=7<BR>\n" );
document.write( "y=5+(7-5)*2=5+4=9<BR>\n" );
document.write( "y=5*(8-5)*2=5+6=11<BR>\n" );
document.write( "y=5+(9-5)*2=5+8=13<BR>\n" );
document.write( "Works every time.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "We could also have <BR>\n" );
document.write( "y=x+(x-5)<BR>\n" );
document.write( "y=5+0<BR>\n" );
document.write( "y=6+1<BR>\n" );
document.write( "y=7+2<BR>\n" );
document.write( "y=8+3<BR>\n" );
document.write( "y=9+4<BR>\n" );
document.write( "Why do they both work?<BR>\n" );
document.write( "reduce the first<BR>\n" );
document.write( "y=5+(x-5)*2<BR>\n" );
document.write( "y=5+2x-10<BR>\n" );
document.write( "y=2x-5\r<BR>\n" );
document.write( "\n" );
document.write( "reduce the second<BR>\n" );
document.write( "y=x+(x-5)<BR>\n" );
document.write( "y=2x-5<BR>\n" );
document.write( "because they both are equal to y=2x-5<BR>\n" );
document.write( "So the best equation is y=2x-5<BR>\n" );
document.write( "which saves on calculations<BR>\n" );
document.write( "y=10-5=5<BR>\n" );
document.write( "y=12-5=7<BR>\n" );
document.write( "y=14-5=9<BR>\n" );
document.write( "y=16-5=11<BR>\n" );
document.write( "y=18-5=13\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );