document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1185462>Question 1185462</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The equation of line passing through origin and perpendicular to line:<BR>\n" );
document.write( "2x + y - 5 = 0 is ____? <BR>\n" );
document.write( "A. 2x + y + 5= 0<BR>\n" );
document.write( "B. x - 2y + 5 = 0<BR>\n" );
document.write( "C. x - 2y - 5 = 0<BR>\n" );
document.write( "D. x + 2y + 5= 0<BR>\n" );
document.write( "E. None of these\r<BR>\n" );
document.write( "\n" );
document.write( "[Note: If answer is option E, then find the exact answer] </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #816303 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=816303\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "(1) You know the answer is E without doing much work; none of the equations in answer choices A to D passes through the origin, because (x,y)=(0,0) is not a solution to any of them.<br><BR>\n" );
document.write( "(2) The method shown by the other tutor for finding the equation of the prescribed line is a good basic algebraic approach.  But when the given equation is in the given form, there is a faster, more sophisticated way to get the answer.<br><BR>\n" );
document.write( "For a given line with equation ax+by=c (c any constant), any line perpendicular to it has an equation of the form bx-ay=d (d is some constant).  Note this equation is obtained by switching the coefficients of x and y in the original equation and changing the sign of one of them.<br><BR>\n" );
document.write( "So, with the given line having equation 2x+y-5=0, we know the equation of any line perpendicular to it has an equation of the form x-2y+c=0.<br><BR>\n" );
document.write( "Then to find the constant c, we use the fact that the origin (0,0) is on the line we want, so (x,y)=(0,0) must satisfy the equation:<br><BR>\n" );
document.write( "x(0)-2(0)+c=0<BR>\n" );
document.write( "0+c=0<BR>\n" );
document.write( "c=0<br><BR>\n" );
document.write( "And the equation we want is<br><BR>\n" );
document.write( "ANSWER: x-2y=0<br><BR>\n" );
document.write( "Here is a graph showing the given line 2x+y-5=0 (red) and the line x-2y=0 (green) that is perpendicular to the given line and passing through the origin.  Also shown are a couple of other lines with equations of the form x-2y=c for different constants c, showing that all those lines are perpendicular to the given line.<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C400%2C-10%2C10%2C-10%2C10%2C-2x%2B5%2C0.5x%2C0.5x%2B2%2C0.5x-6%29 ALIGN=MIDDLE  ALT=\"graph%28400%2C400%2C-10%2C10%2C-10%2C10%2C-2x%2B5%2C0.5x%2C0.5x%2B2%2C0.5x-6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );