SOLUTION: I'm trying to find the perpendicular line to 2x+3y=6 I know in order to find a perpendicular line you need to get the reciprocal but I'm not sure what I need to flip and turn in

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Question 308811: I'm trying to find the perpendicular line to 2x+3y=6
I know in order to find a perpendicular line you need to get the reciprocal but I'm not sure what I need to flip and turn into a negative. I tried writing it in y=mx+b form, but not really sure where to go from here. This is what I have so far.
2x+3y=6
-2x -2x
________
3y=-2x+6
--------
3 3 3
y=-2x+2
-
3

Not really sure the best way to show that I divided by 3 and how to write the fraction
-2x
-
3
So thats how I did it, hope it makes sense :)
After playing around on a graph I found the answer is
y=2x-2
-
3
but I don't know how to get that!
Answer by Fombitz(32388) (Show Source):
You can put this solution on YOUR website!
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,

So then the negative reciprocal would be the slope of the perpendicular line.

Use the slope-intercept form,

If you have a point that needs to be on the new line, you would then use it here to solve for b.

Any b will yield a line that is perpendicular to the original line.
Here's a graph when