Show the code you have so far and explain what the pieces are that relate to it and what it needs to control.

In your startDragging function you can establish a MOUSE_MOVE event listener and use its event handler function to adjust the animation to the position of the sliderKnob.

If your animation is frame-based, then you need to use the position of the knob relative to its total moveable distance and adjust the frame of the animation to be the same... that means if the slider is 25% of the way along its path, then the animation should be at the frame that represents 25% of the frames that comprise it... the relationship is along the lines of...

knob.x / track.width = animation.currentFrame / animation.totalFrames;

or....

animation.currentFrame = animatio.totalFrames * knob.x / track.width;

you'll just have to use some rounding to key the results as integer values for the frames.

In your stopDragging function you remove the MOUSE_MOVE listener.

Here is the code with the adjustments made to move the animation.  Since you say you understand the math behind the equation, I am leaving that part for you to work out...

import flash.geom.Rectangle;
import flash.events.MouseEvent;

var knobWidth:Number = sliderKnob.width;
var trackWidth:Number = sliderTrack.width;
var trackX:Number = sliderTrack.x;         
var boundWidth = trackWidth - knobWidth;
var boundsRect:Rectangle = new Rectangle(trackX, 0, boundWidth, 0);

sliderKnob.addEventListener(MouseEvent.MOUSE_DOWN, startDragging);

sliderKnob.addEventListener(MouseEvent.MOUSE_UP, stopDragging);

sliderKnob.addEventListener(MouseEvent.MOUSE_OUT, stopDragging);

// these are event handler functions...
// the functions that get executed when an event occurs

function startDragging(event:MouseEvent) {
   sliderKnob.startDrag(false, boundsRect);
   stage.addEventListener(MouseEvent.MOUSE_MOVE, moveAnimation);
}

function stopDragging(event:MouseEvent) {
   sliderKnob.stopDrag();

   stage.removeEventListener(MouseEvent.MOUSE_MOVE, moveAnimation);
}

function moveAnimation(evt:MouseEvent):void {
   animation.gotoAndStop( you determine this );
}