What is the slope of 2x-3y+7=0

2x-3y+7=0 -- add 3y to both sides
3y=2x+7 -- divide by 3
y=2x/3 +7/3

The gradient is 2/3

So we move the constant and the x(or the slope) to the right side making

-3y=-2x-7

then we divide by -3

y=(2/3)x+7/3

our slope is 2/3 because in the equation we show this:
y=m(x)+b 

where m is slope and b is intercept