Clutch cable problem...maybe?

The bike is a mostly stock 1982 KZ750H3 LTD. In the last few months I've noticed that when I pull in the clutch and shift to low (or any other gear) the bike tries to pull and I have to hold the brake to keep it still. I tried adjusting the cable at the lever, which had only a little slack. I took all the slack out of it (no, I won't leave it that way) and she still tries to pull, though not quite as bad. I looked at the cable and it looks fine, not worn or frayed, though I don't know how old it is.

It shifts fine and so far the clutch is still strong.

I'm worried as this probably means slipping in the clutch when it happens. What can I do about this? Seems to be another adjustment part way down the clutch cable but I'm not sure how it works.

Any advice? Thanks!

The other adjuster (part way down the clutch cable) is the same as the adjuster at your lever if you take a good look at it you will see that its just a locknut.Loosen it off and turn the threads out(spread them apart)you will soon see the play in your clutch cable tightened up then run the jam nut up to where it was before and tighten it up should be good to go.Dont over tight it you may have to adjust it in the future.(have you ever owned a bike B4)

If not already done, would perform clutch pushrod adjustment.

Good Fortune!

Clutch pushrod adjustment is a little more in depth
Take off the clutch cover,in the middle of the clutch assy youll find a slotted rod with a jam nut on it.Loosen off the jam nut turn the slotted rod until clutch play is resolved then torque it back up.Also be aware that instead of buying new clutch springs a washer of the same size at all 5 bolts will make a worn clutch useable again.as long as you have about 35 to 40 lbs of compression youll be ok.However reading what you wrote I think you just gotta adjust your cable buy the sounds of it.GOOD LUCK