document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=521342>Question 521342</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Write an equation of the line contaning the given point and perpendicular to the givin line <BR>\n" );
document.write( "(3,-6); 4x+9y=7 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #346442 by </B><A HREF=/tutors/aboutme.mpl?userid=Maths68><B>Maths68(1474)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Maths68><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=Maths68><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=346442\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Given<BR>\n" );
document.write( "Point (x, y)=(3,-6) <BR>\n" );
document.write( "Line: 4x+9y=7<BR>\n" );
document.write( "Rearrange the equation according to equation of standard form <BR>\n" );
document.write( "4x+9y=7<BR>\n" );
document.write( "9y=-4x+7<BR>\n" );
document.write( "9y/9=(-4x+7)/9<BR>\n" );
document.write( "y=(-4/9)x+7/9<BR>\n" );
document.write( "Compare above equation with the equation of line slope-intercept form<BR>\n" );
document.write( "y=mx+b\r<BR>\n" );
document.write( "\n" );
document.write( "m=-4/9  and b=7/9<BR>\n" );
document.write( "Slope of the given line m =-4/9 and y-intercept = b =7/9\r<BR>\n" );
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document.write( "Since required line is perpendicular, the multiplication of the slopes of both lines result in (-1), therefore the slope of the required line will be (9/4)<BR>\n" );
document.write( "================================================================<BR>\n" );
document.write( "Now we have a point (3,-6) and slope (9/4) of the required line we can easily find the required line put these values in the equation of slope-intercept form to find the y-intercept of the required line<BR>\n" );
document.write( "y=mx+b<BR>\n" );
document.write( "-6=(9/4)(3)+b<BR>\n" );
document.write( "-6=27/4+b<BR>\n" );
document.write( "-6-27/4=b<BR>\n" );
document.write( "-24-27/4=b<BR>\n" );
document.write( "-51/4=b<BR>\n" );
document.write( "b=-51/4\r<BR>\n" );
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document.write( "y-intercept of the required line =b=-51/4<BR>\n" );
document.write( "================================================================<BR>\n" );
document.write( "Put the values of ‘m’ and ‘b’ in equation of the line slope-intercept form<BR>\n" );
document.write( "y=mx+b<BR>\n" );
document.write( "y=(9/4)x-51/4<BR>\n" );
document.write( "Above equation is the required equation of the line<BR>\n" );
document.write( "Red Line = y =(-4/9)x+7/9<BR>\n" );
document.write( "Green Line = y =(9/4)x-51/4 \r<BR>\n" );
document.write( "\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );