document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=70884>Question 70884</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0078603900/algebrahomeworkh></A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\">                write equation in standard form\r<BR>\n" );
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document.write( "                   y+11=1/3(x+3) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #50649 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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=50649\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The standard form of an equation is:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Ax+%2B+By+=+C ALIGN=MIDDLE  ALT=\"Ax+%2B+By+=+C\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "The equation you were given is:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%2B11=%281%2F3%29%2A%28x%2B3%29 ALIGN=MIDDLE  ALT=\"y%2B11=%281%2F3%29%2A%28x%2B3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "One of the first things we can do is to get rid of the denominator of the fraction on the<BR>\n" );
document.write( "right side. We do this by multiplying all terms on both the left and right side of the equation<BR>\n" );
document.write( "by 3. On the right side when you multiply 3 times <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F3 ALIGN=MIDDLE  ALT=\"1%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > the result is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2F3 ALIGN=MIDDLE  ALT=\"3%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "which just becomes <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" > and multiplying that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" > by (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B3 ALIGN=MIDDLE  ALT=\"x%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" > results in the whole<BR>\n" );
document.write( "right side being reduced to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B3 ALIGN=MIDDLE  ALT=\"x%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  Multiplying the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%2B11 ALIGN=MIDDLE  ALT=\"y%2B11\"   DISABLED_style= \"max-width:90%; height:auto;\" > on the left side <BR>\n" );
document.write( "results in the left side becomes <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3y+%2B+33 ALIGN=MIDDLE  ALT=\"3y+%2B+33\"   DISABLED_style= \"max-width:90%; height:auto;\" >. So the problem is now in the form:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3y+%2B+33+=+x+%2B+3 ALIGN=MIDDLE  ALT=\"3y+%2B+33+=+x+%2B+3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Now look at the standard form.  The terms containing the letter variables x and y are<BR>\n" );
document.write( "alone on the left side and the constants are combined on the right side.  So now let's<BR>\n" );
document.write( "get both the lettered terms on the left side.  To do that we need to get rid of the x<BR>\n" );
document.write( "on the right side of the equation.  We do that by subtracting x from the right side.<BR>\n" );
document.write( "But if we do that we also have to subtract x from the right side.  When we do that the<BR>\n" );
document.write( "equation becomes:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-x+%2B+3y+%2B+33+=+3 ALIGN=MIDDLE  ALT=\"-x+%2B+3y+%2B+33+=+3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "We are getting closer to the standard form.  Now notice that we have a 33 on the left<BR>\n" );
document.write( "side, but this is a constant and we need to have all the constants lumped together <BR>\n" );
document.write( "on the right side. So let's subtract 33 from the left side.  To do that we also need to<BR>\n" );
document.write( "subtract 33 from the right side. After we do that the resulting equation is:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-x+%2B+3y+%2B+-30 ALIGN=MIDDLE  ALT=\"-x+%2B+3y+%2B+-30\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "That's it. Compare this to the standard form that was given at the start of this response <BR>\n" );
document.write( "and you will notice that they are both in the same form.<BR>\n" );
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document.write( "Hope this helps you to understand the standard form a little better and how to move<BR>\n" );
document.write( "things around in an equation to get that equation into standard form. </SPAN>\n" );
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