document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1102011>Question 1102011</A>: <I><SPAN STYLE=\"word-break: break-all;\"> What is an equation of the line that passes through the point (5,5) (5,5) and is perpendicular to the line 5x+4y=365x+4y=36? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #716692 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=716692\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "Something in the way you type your message is causing all the numbers and algebraic expressions to show up doubled.  Where you specify the point (5,5), we see in the message (5,5) (5,5); where you specify the equation 5x+4y=36, we see 5x+4y=365x+4y=36.<br><BR>\n" );
document.write( "The given line has the equation 5x+4y = 36; we are to find the equation of the line through (5,5) perpendicular to the given line.<br><BR>\n" );
document.write( "For the given equation, every line parallel to the given line will have an equation of the form 5x+4y=c for come constant c -- that is, the coefficients of both x and y stay the same.<br><BR>\n" );
document.write( "Every line perpendicular to the given line will have an equation of the form 4x-5y=c for some constant c.  Look what happened to the coefficients -- they traded places, and one of them changed sign.<br><BR>\n" );
document.write( "You can get the same result by finding the slope of the given line and taking the negative reciprocal to get the slope of the perpendicular line; but just altering the coefficients as described saves time.<br><BR>\n" );
document.write( "So the line we are looking for has an equation of the form 4x-5y=c; if it passes through the point (5,5), then x=5 and y=5 must satisfy the equation.  So<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%285%29-5%285%29+=+20-25+=+-5+=+c ALIGN=MIDDLE  ALT=\"4%285%29-5%285%29+=+20-25+=+-5+=+c\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So we know the equation we are looking for is 4x-5y = -5. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );