document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=314687>Question 314687</A>: <I><SPAN STYLE=\"word-break: break-all;\"> find the equation of the line through (1,5) perpendicular to 4x+3y=15. write answer in slope intercept form </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #225050 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=225050\">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( "<b>Step 1:</b>  Determine the slope of the given line.  If the given equation is in Standard Form, i.e. <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large Ax\ +\ By\ =\ C\">, take the additive inverse of the coefficient on <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\"> divided by the coefficient on <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large y\">.  If the given equation is in slope-intercept form, i.e. <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large y\ =\ mx\ +\ b\">, then just take the coefficient on <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\">.  If the given equation is in some other form, put it into slope-intercept form and use 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( "<b>Step 2:</b>  Determine the slope of the desired line.  If you want a parallel line, use the slope of the given line, 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\ \parallel\ L_2 \ \ \Leftrightarrow\ \ m_1\ =\ m_2\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "If you want a perpendicular line, use the negative reciprocal of the slope of the given line, 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( "<b>Step 3:</b>  Use the point-slope form of the equation of a line:\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)\"> are the coordinates of the given point and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large m\"> is the slope derived in step 2.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<b>Step 4</b>:  If you are not asked to put the equation in any particular form, you are done.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "If you are asked to put the equation into slope intercept form, do the required algebra to rearrange the results of Step 3 to the form:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<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( "If you are asked to put the equation into Standard Form, do the required algebra to rearrange the results of Step 3 to the form:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ Ax\ +\ By\ =\ C\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Note:  Some textbooks require <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large A\ \in\ \mathbb{Z}\">, <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large B\ \in\ \mathbb{Z}\">, and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large C\ \in\ \mathbb{Z}\">\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" );