9x-2y=6
what is this equation in slope intercept form?

When you are asked to represent an equation in slope intercept form, we want it to resemble y=mx+b, where the y alone is one the left side, and everything else is on the other side. First, we need to subtract 9x from both sides to isolate the 2y.
-2y=6-9x

Then, we need to divide both sides by -1 to get rid of the negative if front of the 2y.
2y=-6+9x or 2y=9x-6

Lastly, we need to divide both sides by 2.
y=9/2y-3 or y=4.5y-3 are both acceptable answers. 

Hope this helps.