Question 251941
2x+3y=12?
3Y=-2X+12
Y=-2X/3+12/3
Y=-2X/3+4 (RED LINE) 
THIS LINE HAS A SLOPE=-2/3.
ALL PERPENDICULAR LINES WILL HAVE A SLOPE=3/2.
ONE SUCH LINE WOULD BE Y=3X/2+4 (GREEN LINE).
{{{ graph( 200, 200, -6, 5, -6, 5, -2x/3 +4, 3x/2 +4) }}} (graph 200x200 pixels, x from -6 to 5, y from -6 to 5, of TWO functions -2x/3 +4 and 3X/2 +4).