document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=534370>Question 534370</A>: <I><SPAN STYLE=\"word-break: break-all;\"> As hard as I try, I have been unable to understand this lesson, much less answer anything correctly. This is an example homework question:\r<BR>\n" );
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document.write( "Write an equation of the line containing the given point and perpendicular to the given line. Express your answer in the form of y=mx+b\r<BR>\n" );
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document.write( "(2, -6); 8x + 5y = 6\r<BR>\n" );
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document.write( "I know that I'm supposed to subtract 8x from both sides (to solve for y), and I am able to complete the first step correctly:\r<BR>\n" );
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document.write( "5y = -8x + 6\r<BR>\n" );
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document.write( "It then tells me to divide each side by 5 (this is where my answer does not match up with the correct homework answer) and I get:\r<BR>\n" );
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document.write( "y =   8        6 <BR>\n" );
document.write( "    - _ x  +   _<BR>\n" );
document.write( "      5        5\r<BR>\n" );
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document.write( "The correct answer is:\r<BR>\n" );
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document.write( "y =    8       29 <BR>\n" );
document.write( "     - __ x  - __<BR>\n" );
document.write( "        5       4\r<BR>\n" );
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document.write( "What am I doing wrong??? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #351493 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=351493\">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( "There are only two ways to derive an equation of a line.  You either need two points that are on the line or one point that is on the line and the slope of the line.\r<BR>\n" );
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document.write( "So let's look at this problem starting at the end and then work backwards.\r<BR>\n" );
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document.write( "Your goal is to write an equation of a line and you are given two pieces of information.  One is a point on the desired line and the other is the equation of a line that is perpendicular to the one you want.  Finding a second point to define the desired line is not possible with the information given, but the equation of the given line will tell us the slope of THAT line.  The fortunate circumstance is that the slopes of perpendicular lines are related in a very special way.  Perpendicular lines have slopes that are negative reciprocals of one another.  That is to say if <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \frac{a}{b}\"> is the slope of a line, then <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large -\frac{b}{a}\"> is the slope of any line perpendicular to it.\r<BR>\n" );
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document.write( "The process you started, namely solving the given equation for <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large y\"> is the first step because once a two variable linear equation is solved for the vertical axis variable (<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large y\">) in terms of the other variable (<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\">), the coefficient on <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\"> <i><b>is</b></i> the slope of the line.  Then to get the slope of the <i><b>desired</b></i> line, just flip the fraction and change the sign.\r<BR>\n" );
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document.write( "Given the point <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large (2,-6)\"> and the line <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large 8x\ +\ 5y\ =\ 6\">, write an equation of a line through the given point perpendicular to the given line.\r<BR>\n" );
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document.write( "Step 1:  Solve the given equation for <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large y\">:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 8x\ +\ 5y\ =\ 6\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 5y\ =\ -8x\ +\ 6\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ y\ =\ -\frac{8}{5}x\ +\ \frac{6}{5}\">\r<BR>\n" );
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document.write( "Which is what you had.  But you weren't done.\r<BR>\n" );
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document.write( "Step 2:  Determine the slope of the given line, which is simply the coefficient on <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\">, namely <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large -\frac{8}{5}\">, and then compute the slope for the desired line.  Flip the fraction and change the sign.  <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \frac{5}{8}\">.\r<BR>\n" );
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document.write( "Step 3:  Use the point-slope form of an equation of a line to write the equation of the desired line:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ y\ -\ y_1\ =\ m(x\ -\ x_1)\">\r<BR>\n" );
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document.write( "where <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \left(x_1,y_1\right)\"> are the coordinates of the given point and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large m\"> is the given/calculated slope. So:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ y\ -\ (-6)\ =\ \frac{5}{8}(x\ -\ 2)\">\r<BR>\n" );
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document.write( "Doing the arithmetic:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ y\ =\ \frac{5}{8}x\ -\ \frac{29}{4}\">\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" );
document.write( "My calculator said it, I believe it, that settles it<BR>\n" );
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