document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=251333>Question 251333</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the equation of the line that contains point (12,-7) and perpendicular to the line whose equation is 4y-3x+9=0 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #183030 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=183030\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Garamond\" size=\"+2\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Sorry, this question cannot be answered exactly as you posed it.  For any given line, there are an infinite number of equations which solution sets are the ordered pairs that comprise the line.  While most are only trivially different, the fact that you can put any two variable linear equation into several forms means there is more than one representation non-trivially different.  Hence, finding \"the\" equation of a line is impossible.  Below a method to find \"an\" equation of the desired line.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Step 1.  Solve the given equation for y in terms of everything else, that is, put it into slope intercept form, <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE y\ =\ mx\ +\ b\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Step 2.  Determine the slope of the line represented by the given equation by inspection of the coefficient on <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE x\">.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Step 3.  Calculate the slope of any line perpendicular to the given line by determining the negative reciprocal of the slope determined in 2 -- because:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
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}\ \text{ and } m_1,\, m_2\, \neq\, 0\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Step 4.  Use the point-slope form of an equation of a line along with the given point and the slope determined in step 3 to write a form of the desired equation.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ y\ -\ y_1\ =\ m(x\ -\ x_1) \">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "where <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \left(x_1,y_1\right)\"> is the given point and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large m\"> is the slope determined in step 3.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Step 5.  If necessary, either because of instructions provided in your text or by your instructor, alter the form of the result of step 4 by normal algebraic means either to the slope-intercept form as discussed in step 1, the standard form, <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE Ax\ +\ By\ =\ C\">, or whatever form is specified.  If no form is specified, then you can certainly consider the problem properly completed if you stop at the end of step 4 -- which is to say that no one can say that the result of step 4, given correctly performed arithmetic and algebraic manipulations, is NOT a representation of the desired line.  (Note: some texts require A, B, and C to be integers for proper standard form)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
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( "</font> </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );