Move container sprite according to mouse movement

Hi All,
Currently I'm developing a game where there is a object which follows mouse. Also there are other objects and a map on the screen.I want all of background content(whole map and other objects) to move when user moves mouse left or right. That is, if user moves mouse on right side then all content(except object which moves as per mouse) should move left side so that user can see remaining part of map on the right side.
As of now I have created new Container sprite in which I have added all of my objects and map. So when user moves the mouse right, I move the container sprite to left so it looks all stuff moves to left. Code looks like as below
var pt:Point = new Point(character.x, character.y);
pt = dori.localToGlobal(pt);
if (pt.x > (stage.width * 0.5))
container.x -= 5;
Structure of project is such that, I add Container directly to stage. and this container contains everything like map, character and other objects.
Now issue is that as soon as mouse goes beyond middle of stage...it creates distance between mouse location and character..!! I mean it does move according to mouse but some distance get created between mouse and character. and this distance keeps increasing as I continue to move mouse away from center of stage!!
I'm really stuck with this issue. Please someone help with this. I hope I have explained this well. Let me know if you need more info but please help.

No see......I dont want ease in n all....and character following the mouse logic is working fine if I dont use above linear interpolation to move the container mc.....
but I do want to move container mc as well so I will have to use what you gave to move the all background objects when user moves mouse....
so Again to clarify, in the game when user moves mouse the character should follow and at the same time bakckground objects which are in container mc should move opposite to mouse movement so that remainng mape gets visible to the user....
just now when I was debuggin the linear interpolation logic...I got to know that there something I need to change in it...because accroding to that logic...let say for example
stageWidth is 480
maze.width is 551
then x1 will be 480
y1 will be -71
x2 will be 0 and
y2 will be 0
so m = (y1 - y2) / (x1 - x2) = -71 - 0 / 480 - 0
m = -0.147
b = y1 - m * x1 = -71 - (-0.147 * 480) = 0
so on each enter frame when mouseX wil be multiplied with m....it will create lag in moving container(character is in container as well!
bcoz
container.x = m * stageRef.mouseX + b;
so I'm confused!!
where do u think shall correction be made??

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