What is the equation of the line that is parallel to the given line and passes through the point (-3,2)

Answer is D, because first you figure out the slope of the line given and you get down 4 right 3 so it will be -4/3. And you are finding the parallel of that line so they have the same slope. So then you plug it into the point slope form so it will lead you to (y-2)=-4/3(x+3). You simplify this by doing the distributive property so you will get y-2=-4/3x-4. Add the 2 to both sides and your looking for the equation y=-4/3-2. To get this equation you look at the given choices and 4 is the top dominator so you need a 4 in for the given x. and the value that it equal needs to be a multiple of 2. So after cancelling those two out you end with 4x+3y=-6