document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=506437>Question 506437</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I'm not sure how to determine whether or not a function is linear. I know and understand what a linear function is, but I'm not sure how to immediately determine it. I know it has something to do with f(x)= mx+b. My teacher taught me something about A, B, and C. I'm not sure what he exactly means by this. The problems I'm having trouble are:\r<BR>\n" );
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document.write( "1. x/2=10+2y/3<BR>\n" );
document.write( "2. 3a+b-2=b<BR>\n" );
document.write( "3. 3m/4= 2n/3-5\r<BR>\n" );
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document.write( "Is there anyway where I can immediately identify it as linear or non-linear without graphing it or testing the function out?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #340160 by </B><A HREF=/tutors/aboutme.mpl?userid=Sarah900><B>Sarah900(12)</B></A><img src=\"/images/stars/stars-06.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Sarah900><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=340160\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A linear equation can be written in the Standard form which is Ax+By=C  The important thing here is that neither x, nor y is in a denominator, radical, or exponent.  They are not multiplied together and they are being taken to an exponent of 1.    For example the first equation can be rewritten as <BR>\n" );
document.write( "x/2-2y/3=10  <BR>\n" );
document.write( "In this case 1/2=A -2/3=B and 10=C\r<BR>\n" );
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document.write( "In the second one the b's cancel leaving<BR>\n" );
document.write( "3a=2<BR>\n" );
document.write( "This is also in standard form.  The B in this case just happens to be 0.\r<BR>\n" );
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document.write( "If you rearrange the last problem you will find it can also be placed in Standard form. </SPAN>\n" );
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