The throttle cable should be fairly tight. If it is loose where it attaches to the throttle arm it should be tightened. On my car (an 86) there is an adjustment at the end of the cable housing. It is a white plastic threaded fitting that can be turned to push the housing back to tighten the cable.
To determine where the slack is, have your wife push on the throttle while you observe the end of the cable where it exits the housing.