document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=558554>Question 558554</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find (a)the equation of the line that is parallel to the given line and includes the given point, and (b) the equation of a line that is perpendicular to the given line through the given point. Wright both answers in slope-intercept form. (c) Graph both of these lines on the same axes. Please show all of your work.\r<BR>\n" );
document.write( "\n" );
document.write( "y=-x+4,(-3,7) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #363099 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=363099\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Parallel lines have equal slopes.  Perpendicular lines have slopes that are negative reciprocals.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "For your part a) note that the given point is on the given line.  Therefore the desired equation is identical to the given equation.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "For your part b) calculate the negative reciprocal of the slope of the given line, then used the point slope form of an equation of a line to derive 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)\"> 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.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Rearrange to put the equation into slope-intercept form, that is:  <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( "For your graphs, you already have one point on each of your lines, namely the given point, so plot that point.  Select a small integer value for <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\">, substitute that value for <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\"> into one of your equations, calculate the value of <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large y\"> that results, create the point <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large(x,y)\"> from the value you selected for <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\"> and the value you calculated for <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large y\">, then plot the point.  Draw a line through the two points.  Repeat for the other equation. \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( "My calculator said it, I believe it, that settles it<BR>\n" );
document.write( "<div  DISABLED_style= \"text-align:center\"><a  rel=nofollow HREF=\"http://outcampaign.org/\" target=\"_blank\"><IMG STYLE=\"max-width:80%;\" src=\"http://cdn.cloudfiles.mosso.com/c116811/scarlet_A.png\" border=\"0\" alt=\"The Out Campaign: Scarlet Letter of Atheism\" width=\"143\" height=\"122\" /></a></div><BR>\n" );
document.write( "</font> </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );