To get the slope the easiest way is to get the equation in slope intercept form y = mx + b where m is the slope
Your first equation is 2x = - 3y + 4 so solve for y
3y = -2x + 4
y = -2/3x + 4/3
Your slope is -2/3
Your second equation is y+6 = 0 and if you solve for y it is y = -6, ie the x is really 0*x which means the slope is 0
Lori