My car shakes when i drive and wobbles back and forth at slow speed what is wrong?

Defective rack and pinion steering gear.

iginition time is set too late, ********, readjust.2) spark plugs are fouled or incorrect gapped. 3) distributors contct poits are dirty or pitted.
God bless you

Check ur tires for tread separation. It's possible one of the tread belts is coming apart

If it is constantly shaking? Sounds like a knot on your tire. Because if it was tie rod end or sway bar then it would stop at certain times. Like slow speeds, or when you turn a little then straighten it back out.
Jack it up and pull on the wheels and if something is loose or worn out it will show up. Feel around the tire for a knot. Lower the jack to where the tire barely clears the ground and spin it. It will hit the ground if there is a knot you cant feel.

check your front end suspension, sometimes something as small as tire pressure will cause this.

When a steering stabilizer goes bad, it will produce the exact wobble you have described. The one where you NEED to slow down to stop it, and then its fine. Its called "Death Wobble" in the car/truck enthusiast world.

Have you checked that? Typically called a steering stabilizer / steering dampener.

Good luck!

Struts and upper strut bushings.

did you ever let somebody check the wheel allignment, it may be the camber shaft.

the tierod makes the car steer. and it will cause these symptoms it will come off and wreck you also, there are other things that could do this also all just as dangerous. you need to drive it slowly to get it fixed. you can look at the parts while a friend wiggles the steering wheel back and forth to see what is loose it will have a lot of play in it.

this is known as death wobble because it feels like you are going to die but slowing down will end it.

The cause for death wobble are:

1. Worn or loose tie rod ends on your steering linkage.
2. Worn or loose trackbar bushings or tie rod ends on the trackbar itself.
3. front end needs alignment.
4. and many others but the common reasons are listed above.

try to realign the front end. If it doesnt help, then you do indeed have worn steering / suspension components.