5y+6x-2=0 ---------------Original Equation
2+5y+6x-2=0+2 --------Add 2 on both sides of the equal sign
5y+6x=2
6x-5y+6x=2-6x----------Subtract 6x on both sides of the equal sign
5/5y= -6x+2/5-------------Divide by 5 on both sides of the equal sign
y= -6/5x+2/5
So the slope would be -6/5.