Question 308811
Best way to show it is like this:
3y=-2x+6
y=(-2x+6)/3
Because then there is no confusion.
OK, so the slope of this line is,
{{{m1=-2/3}}}
So then the negative reciprocal would be the slope of the perpendicular line.
{{{m2=3/2}}}
Use the slope-intercept form,
{{{y=(3/2)x+b}}}
If you have a point that needs to be on the new line, you would then use it here to solve for b. 
{{{b=y-(3/2)x}}}
Any b will yield a line that is perpendicular to the original line. 
Here's a graph when {{{b=0}}}
{{{ graph( 300, 300, -5, 5, -5, 5, (-2x+6)/3, (3/2)x) }}}