document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1182992>Question 1182992</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the equation of the straight line which<BR>\n" );
document.write( "passes through the point(-3,5) and is<BR>\n" );
document.write( "perpendicular to the line 2x-4y+3=0?<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #813123 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=813123\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "Using basic algebra....<br><BR>\n" );
document.write( "(1) Find the slope of the given line<br><BR>\n" );
document.write( "2x-4y+3=0<BR>\n" );
document.write( "4y = 2x+3<BR>\n" );
document.write( "y = (1/2)x+3/4<br><BR>\n" );
document.write( "The slope is 1/2; the slope of a line perpendicular to that line is -2/1, or just -2.<br><BR>\n" );
document.write( "(2) Use the general slope-intercept form of the equation with the desired slope of -2 passing through (x,y) = (-3,5) to find the equation<br><BR>\n" );
document.write( "y = mx+b<BR>\n" );
document.write( "5 = (-2)(-3)+b<BR>\n" );
document.write( "5 = 6+b<BR>\n" );
document.write( "b = -1<br><BR>\n" );
document.write( "ANSWER: y = -2x-1<br><BR>\n" );
document.write( "A faster path to the answer....<br><BR>\n" );
document.write( "Given the equation 2x-4y+3=0, any line parallel to that line has the form 2x-4y+C=0 for some constant C, and any line perpendicular to that line has the form 4x+2y+C=0 for some constant C (switch the coefficients of x and y and change the sign of one of them).<br><BR>\n" );
document.write( "So we are looking for an equation of the form 4x+2y+C=0 that is satisfied by (x,y) = (-3,5):<br><BR>\n" );
document.write( "4(-3)+2(5)+C=0<BR>\n" );
document.write( "-12+10+C=0<BR>\n" );
document.write( "C=2<br><BR>\n" );
document.write( "The equation we want is<br><BR>\n" );
document.write( "4x+2y+2=0<br><BR>\n" );
document.write( "That is equivalent to the answer we got using basic algebra:<br><BR>\n" );
document.write( "4x+2y+2=0<BR>\n" );
document.write( "2y = -4x-2<BR>\n" );
document.write( "y = -2x-1<br><BR>\n" );
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