First off, thank you for being a MHF donor!
Alright let's get to the math.
1. The concept of slope is how many units are the y-values changing for every x-value. And for this we have a nice formula.
S_line = (y2-y1)/(x2-x1)
Does this look familiar?
2. The form that we use to easily graph lines is: y = mx + b. So let's try to isolate y.
3x + 2y = 6
2y = 6 - 3x
y = 3 - (3/2)x OR y = (-3/2)x + 3
Can you graph it now?
3. When a line is the form used earlier, y = mx + b, the "m" value represents the slope. Here, m = -9 and b = 0. So the slope is -9. The y-intercept occurs where x=0, so plug in 0 for x and see where this happens.