Simple, you are confusing about background method:

1. public void setup() {
           size(500, 500);
       }
   
       public void draw() {
           stroke(0, 0, 0, 100);
           strokeWeight(20);
           line(this.mouseX, this.mouseY, this.pmouseX, this.pmouseY);
       }

is different from this:

1. public void setup() {
           size(500, 500);
       }
   
       public void draw() {
           background(0); // <-------ERROR-------->
           stroke(0, 0, 0, 100);
           strokeWeight(20);
           line(this.mouseX, this.mouseY, this.pmouseX, this.pmouseY);
       }

background() is placed first because Processing is an 'extension' of JAVA language, and the things need to be an order of execution;

draw() method reads each of methods in order, during sketch lifecycle ( repeatedly, in frames per second), so to your code works as expected, the first thing that need to be updated is background;

if background() method is not provided, your background will not be update, therefore you will see these things

the line draws with the alpha but a lot of ellipses inside the trace

In fact, I do not think they are actually balls; they are pieces of a line that sought to be drawn, but turned remnant, and appear ball because you use strokeWeight() method

(vc é brasileiro?)

Hi!

I know about the background(), in the actual program I'm using an image as background

As you found out, the ellipses are only the result of superposing the lines with transparency: since each one start where the previous ended, there is some overlay. You can change the effect with strokeCap(), but it won't really disappear.
An alternative, even more if you need to draw over a background, is indeed to store the points in an ArrayList, and redraw them on each draw().

Or maybe you could use a PGraphic buffer and draw that overtop - have the background in the default buffer then the line in the PGraphic ??

I've tried with strokeCap() already but it don't disappear =/

here's a short piece of code, that uses an arraylist

1. ArrayList<PVector> polyline = new ArrayList<PVector>();
2. void setup(){
3.   size(400, 400); 
4.   smooth();
5. }
6. void draw(){
7.   background(255);
8.  
9.   // add current mouse position to arraylist
10.   polyline.add(new PVector(mouseX, mouseY));
11.  
12.   // styles
13.   noFill();
14.   strokeJoin(ROUND);
15.   stroke(0,0,255, 100);
16.   strokeWeight(10);
17.  
18.   //finally draw the polyline
19.   beginShape();
20.     for(PVector p : polyline){
21.       vertex(p.x, p.y);
22.     }
    
23.   endShape();
24. }

Thank you!
It works, just miss the alpha increasing when the line crosses itself