document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=837215>Question 837215</A>: <I><SPAN STYLE=\"word-break: break-all;\"> sir please help me i badly need it now.. thanks..<BR>\n" );
document.write( "Find the equation of the line through (-3,5) which makes the angle of 45 degrees with the line 2x+y=12 . its analytic geometry sir.. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #504543 by </B><A HREF=/tutors/aboutme.mpl?userid=LinnW><B>LinnW(1048)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=LinnW><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=LinnW><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=504543\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \r<BR>\n" );
document.write( "\n" );
document.write( "Let's find the equation of a line through (-3,5)<BR>\n" );
document.write( "that is perpendicular to y = -2x + 12\r<BR>\n" );
document.write( "\n" );
document.write( "First find the slope of 2x + y = 12<BR>\n" );
document.write( "add -2x to each side<BR>\n" );
document.write( "y = -2x + 12<BR>\n" );
document.write( "slope is -2<BR>\n" );
document.write( "so slope of perpendicular is 1/2<BR>\n" );
document.write( "To find the slope of a line that is 45 degrees<BR>\n" );
document.write( "offset, consider equations with slopes -2 and 1/2<BR>\n" );
document.write( "the pass through (0,0)<BR>\n" );
document.write( "y =-2x and y = (1/2)x<BR>\n" );
document.write( "Let L = the length of the segment between<BR>\n" );
document.write( "(0,0) and (1,-2) , points on the line y = -2x<BR>\n" );
document.write( "The length of the segment between<BR>\n" );
document.write( "(0,0) and (2,1) is equal L and on the line y = (1/2)x<BR>\n" );
document.write( "The segment between (0,0) and the midpoint<BR>\n" );
document.write( "between (1,-2) and (2,1) will bisect the two lines<BR>\n" );
document.write( "and the angle will be 45 degrees from each.<BR>\n" );
document.write( "The midpoint is ( (1+2)/2 , (-2+1)/2 )<BR>\n" );
document.write( "= ( 3/2 , -1/2)<BR>\n" );
document.write( "The slope of the line through (0,0) and ( 3/2 , -1/2 )<BR>\n" );
document.write( "is (-1/2)/(3/2) = -1/3<BR>\n" );
document.write( "A line though (-3,5) with a slope of -1/3 will<BR>\n" );
document.write( "be 45 degrees offset from 2x+y=12<BR>\n" );
document.write( "y = mx + b<BR>\n" );
document.write( "5 = (-1/3)(-3) + b<BR>\n" );
document.write( "5 = 1 + b<BR>\n" );
document.write( "4 = b<BR>\n" );
document.write( "Our equation is y = (-1/3)x + 4<BR>\n" );
document.write( "Check out the following link to see the plot.<BR>\n" );
document.write( "http://www.wolframalpha.com/input/?i=plot+y%3D-x%2F3+%2B4++and+2x%2By%3D12<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );