document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=181845>Question 181845</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Write an equation of the line that is perpendicular to the line y=-2/3x+4 and passes through the point (1,-4). </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #136444 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=136444\">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( "Perpendicular lines have slopes that are negative reciprocals, that is:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \text{          }\math L_1 \perp L_2 \ \ \Leftrightarrow\ \ m_1 = -\frac{1}{m_2}\">\r<BR>\n" );
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document.write( "Since your given equation is already in slope-intercept form:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \text{          }\math y = mx + b\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \text{          }\math y = -\frac{2}{3}x + 4\">\r<BR>\n" );
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document.write( "You can read the slope directly, i.e. <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large m_1 = -\frac{2}{3}\">\r<BR>\n" );
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document.write( "Therefore any perpendicular line must have a slope:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \text{          }\math m_2 = -\frac{1}{-\frac{2}{3}} = \frac{3}{2} \">\r<BR>\n" );
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document.write( "Now that you have the slope of the desired line along with the given point, <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large P_1(x_1,y_1) = (1, -4)\">, you can use the point-slope form of the equation of a line:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \text{          }\math y - y_1 = m(x - x_1)\">\r<BR>\n" );
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document.write( "where <i>m</i> is the slope and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large (x_1,y_1)\"> is the given point to develop your desired equation:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \text{          }\math y - (-4) = \frac{3}{2}(x - 1)\">\r<BR>\n" );
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document.write( "Since your given equation was in slope-intercept form, you should rearrange your answer to that form as well.\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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