document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=184354>Question 184354</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0201773414/algebrahomeworkh>introductory and intermediate algebra</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> This is on page 542 number 9\r<BR>\n" );
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document.write( "The question is Find an equation of the line containing the point(5,4) and perpendicular to the line 2x - 4y = 12<BR>\n" );
document.write( "I tried to solve this and this is how I did it \r<BR>\n" );
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document.write( "2x - 4y = 12<BR>\n" );
document.write( "-2x        -2x<BR>\n" );
document.write( "-4y = -2x + 12<BR>\n" );
document.write( "then i divided both side by -4<BR>\n" );
document.write( "y = 4/2x + -3<BR>\n" );
document.write( "so then I plugged that in to the next equation\r<BR>\n" );
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document.write( "y - 4 = 4/2(x - 5)<BR>\n" );
document.write( "y - 4 = 4/2x -20/5<BR>\n" );
document.write( "then I added 4 to both sides<BR>\n" );
document.write( "y = 4/2x - 0<BR>\n" );
document.write( " I got this wrong and I do not understand how I did it wrong can you please try to help me? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #138388 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=138388\">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 have three errors:\r<BR>\n" );
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document.write( "First, when you divided by -4 when deriving the slope-intercept form of the given equation, you should have had a result like this:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \ \ y = \frac{2}{4}x - 3 \ \ \Rightarrow\ \ y = \frac {1}{2}x - 3\">\r<BR>\n" );
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document.write( "Rather than\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \ \ y = \frac{4}{2}x - 3 \ \ \Rightarrow\ \ y = 2x - 3\">\r<BR>\n" );
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document.write( "Second you used the same slope number for your derived equation that you developed when you put your given equation in slope-intercept form.  What you developed was an equation for a line <i><b>parallel</b></i> to your incorrect slope-intercept version of the given equation rather than perpendicular to the given line.\r<BR>\n" );
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document.write( "You forgot the rule that perpendicular lines have slopes that are negative reciprocals of each other, or:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \ \ L_1 \perp L_2 \ \ \Leftrightarrow\ \ m_1 = \frac{-1}{m_2}\">\r<BR>\n" );
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document.write( "In your case, <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large m_1 = \frac{2}{4} = \frac {1}{2}\">, therefore <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large m_2 = \frac{-1}{\frac{1}{2}} = -2\">\r<BR>\n" );
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document.write( "And your derived equation should look like:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \ \ y - 4 = -2(x - 5) \ \ \Rightarrow\ \ y = -2x + 10 + 4 \ \ \Rightarrow\ \ y = -2x + 14\">\r<BR>\n" );
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document.write( "Third, when you went from:\r<BR>\n" );
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document.write( "y - 4 = 4/2(x - 5)\r<BR>\n" );
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document.write( "to\r<BR>\n" );
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document.write( "y - 4 = 4/2x -20/5\r<BR>\n" );
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document.write( "You multiplied the -5 by 4 but then forgot to divide by 2.  Your result should have been\r<BR>\n" );
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document.write( "y - 4 = 4/2x - 10/5\r<BR>\n" );
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document.write( "Having said all of that, you really have the right idea about all of this.  You just made a couple of easy-to-make mistakes.  Keep up the good work.\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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