document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=248596>Question 248596</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How do you determine if equations are linear or not and if they are linear how do you write them in standard form? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #181158 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=181158\">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( "Linear equations are of degree 1.  The degree of an equation is the largest SUM of the exponents on any term.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ x\ +\ y\ = 5\">\r<BR>\n" );
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document.write( "is linear because an equivalent form is:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ x^1\ +\ y^1\ =\ 5\">\r<BR>\n" );
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document.write( "And the largest exponent is 1, hence the degree of the equation is 1.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ xy\ =\ 3\">\r<BR>\n" );
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document.write( "is NOT linear.  Look at the equivalent form:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ x^1y^1\ =\ 3\">\r<BR>\n" );
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document.write( "The degree of a term is the SUM of the exponents in that term, hence the <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE xy\"> term is of degree 2, therefore the equation is of degree 2, and therefore not linear.\r<BR>\n" );
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document.write( "Note that <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE x\ =\ \frac{3}{y}\"> is equivalent to the above non-linear equation and is also non-linear.\r<BR>\n" );
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document.write( "Obviously, any equation that has higher powers is also non-linear.  Included in the non-linear category are exponential, logarithmic, and \r<BR>\n" );
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document.write( "The standard form of a two-variable linear equation is:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ Ax\ +\ By\ = C\">\r<BR>\n" );
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document.write( "Some texts require that A, B, and C be integers for proper standard form.\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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