document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=632927>Question 632927</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Can you help me please? How can you determine if 8x=6y+7 as a linear equation with two variables? Is the equation a linear equation in two variables? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #398590 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=398590\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 8x = 6y + 7 is a linear equation in 2 variables.<BR>\n" );
document.write( "you have 2 variables, x and y.<BR>\n" );
document.write( "the highest exponent for any variable in the equation is 1.<BR>\n" );
document.write( "note that x is equivalent to x^1 and y is equivalent to y^1.<BR>\n" );
document.write( "to convert this equation to standard form of a linear equation, subtract 6y from both sides of the equation to get:<BR>\n" );
document.write( "8x - 6y = 7<BR>\n" );
document.write( "to convert this equation to slope intercept form of a linear equation, subtract 8x from both sides of the equation to get:<BR>\n" );
document.write( "-6y = -8x + 7<BR>\n" );
document.write( "multiply both sides of this equation by -1 to get:<BR>\n" );
document.write( "6y = 8x - 7<BR>\n" );
document.write( "divide both sides of this equation by 6 to get:<BR>\n" );
document.write( "y = (8x-7)/6 which is then simplified to:<BR>\n" );
document.write( "y = (8/6)x - (7/6) which is then further simplified to:<BR>\n" );
document.write( "y = (4/3)x - (7/6)<BR>\n" );
document.write( "an equation is linear if the highest exponent of any term in the equation is equal to 1.<BR>\n" );
document.write( "note that we are talking about a polynomial equation which requires that all exponents not be negative and be integers.<BR>\n" );
document.write( "under these rules, x^0 is the lowest exponent that can be used.<BR>\n" );
document.write( "note that x^0 = 1<BR>\n" );
document.write( "some linear equations under these rules are:<BR>\n" );
document.write( "y = 5 (exponent of y is 1 and 5 is a constant)<BR>\n" );
document.write( "x = 5 (exponent of x is 1 and 5 is a constant)<BR>\n" );
document.write( "y = 5x (exponent of x is 1 and exponent of y is 1)<BR>\n" );
document.write( "y = 5x - 13 (exponent of x is 1 and exponent of y is 1 and -13 is a constant)\r<BR>\n" );
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document.write( "note that y = 5x could also be written as -5x + y = 0 and could also be written as 5x = y<BR>\n" );
document.write( "note that y = 5x - 13 could also be written as -5x + y = -13 and could also be written as -5x = -y - 13\r<BR>\n" );
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document.write( " </SPAN>\n" );
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