document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=179219>Question 179219</A>: <I><SPAN STYLE=\"word-break: break-all;\"> if I am graphing a linear equation and the answer is <BR>\n" );
document.write( "-x=9 does that mean that the answer changes to x=9 since x can not be negative or do I have this mixed up with something else.\r<BR>\n" );
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document.write( "I have to graph the linear equation which is -x=-8y+9<BR>\n" );
document.write( "When I do it I did it this way<BR>\n" );
document.write( "-x=-8y+9<BR>\n" );
document.write( "-x=-8*1+9<BR>\n" );
document.write( "-x=-8+9<BR>\n" );
document.write( "-x=1 is the answer, but does this change if there is a rule that you can not have a negative x????? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #134162 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=134162\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
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document.write( "You must have it mixed up with something else that you probably should forget anyway.  If you don't want <i>x</i> to be negative, then you have to do something to it to make it not negative.  But if you do anything to one side of an equation, then you must do the same thing to the other side in order to maintain equality between the two expressions. \r<BR>\n" );
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document.write( "If <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large -x = 9\"> then you need to multiply both sides of the equation by -1 to get <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large (-1)(-x) = (-1)(9) \rightarrow x = -9\"> \r<BR>\n" );
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document.write( "As to your description of your process with <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large -x=-8y+9\">, I think you have things backwards.  Generally, <i>x</i> is the independent variable, and  <i>y</i> is the dependent variable.  That means that you should be selecting values for <i>x</i> and then solving for the value of <i>y</i> that depends upon that selection.  Your first step should be to solve (rearrange) the equation so that you have the value of <i>y</i> in terms of <i>x</i>, thus:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large -x=-8y+9\">\r<BR>\n" );
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document.write( "Add 8y and x to both sides:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large -x + x + 8y = -8y + 8y + x + 9\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large 8y = x + 9\">\r<BR>\n" );
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document.write( "Multiply both sides by <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \frac {1}{8}\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \left(\frac {1}{8}\right) 8y = \left(\frac {1}{8}\right) (x + 9)\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large y = \left(\frac {1}{8}\right) (x + 9)\">\r<BR>\n" );
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document.write( "Now you can select values for <i>x</i> and determine the resulting value for <i>y</i>.\r<BR>\n" );
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document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x = 1 \rightarrow y = \frac {10}{8} = \frac {5}{4}\">\r<BR>\n" );
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document.write( "Therefore the ordered pair <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large (x, y) = (1, \frac {5}{4})\"> is one point on the line.\r<BR>\n" );
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document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x = -1 \rightarrow y = \frac {8}{8} = 1\">\r<BR>\n" );
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document.write( "Therefore the ordered pair <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large (x, y) = (-1, 1)\"> is a second point on the line giving you sufficient information to uniquely determine, and therefore graph, the line by plotting the two points and drawing the line that contains both of them.\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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