Here's a sample from my website.  Probably doing more than you need, but hopefully you can make use of the basic structure.

I think I described by issue poorly. The problem I am having is making the source of the particles move horizontally to the left not just make the particles emit horizontally.

I'm making smoke coming from a smoke stack type building but I'm basically subtracting .5 from the "x" value within the draw function such that the background moves to the left. I just can't seem to make the particle system move as a whole with the rest of the background.

I may be missing something basic but I've tried a lot of things. Thanks again!

I would suggest posting some source - much easier to modify something that is slightly broken than to write it from scratch :)

1. float x = 0;
   float y = 50;
   float a = 15;
   
   //declare a particle system
   PSys fireW1;
   
   int frame;
   
   
   void setup() {
     size(1300, 400);
     smooth();
   
     fireW1 = new PSys(100, new PVector(x + 1000, 100, 0));
   }
   
   class Particle {
    
     PVector loc;
     PVector vel;
     PVector accel;
     float r;
     float life;
   
    
     //constructor
     Particle(PVector a, PVector v, PVector l, float r_) {
       accel = a.get();
       vel = v.get();
       loc = l.get();
       r = r_;
       life = 150;
     }
    
     Particle(PVector l) {
       accel = new PVector(0, -.0005, 0); //gravity
       vel = new PVector(random(0, 1), random(-2, 0), 0);
       loc = l.get();
       r = 10.0;
       life = 150;
     }
    
     //what to do each frame
     void run() {
       updateP();
       renderP();
     }
    
     //a function to update the particle each frame
     void updateP() {
       vel.add(accel);
       loc.add(vel);//add velocity to locaton//
       life -= 2.0;
     }
    
     //how to draw a particle
     void renderP() {
         ellipseMode(CENTER);
         stroke(100, life);
         fill(100, life);
         ellipse(loc.x, loc.y, r, r);
     }
    
     //a function to test if a particle is alive
     boolean dead() {
       if (life <= 0.0) {
         return true;
       } else {
         return false;
       }
     }
   } //end of particle object definition
   
   
   //now define a group of particles as a particleSys
   class PSys{
    
     ArrayList particles; //all the particles
     PVector source; //where all the particles emit from
    
     //constructor
     PSys(int num, PVector v) {
       particles = new ArrayList();
       source = v.get();
       for (int i=0; i < num; i++) {
         particles.add(new Particle(source));
       }
     }
      
       //what to do each frame
       void run() {
         //go through backwards for deletes
         for (int i=particles.size()-1; i >=0; i--) {
           Particle p = (Particle) particles.get(i);
           p.loc.x += p.vel.x;
           //update each particle per frame
           p.run();
           if (p.dead()) {
             particles.remove(i);
           }
         }
       }
      
       void addParticle() {
         particles.add(new Particle(source));
       }
      
       void addParticle(Particle p) {
         particles.add(p);
       }
      
       //is particle system still populated?
       boolean dead() {
           if (particles.isEmpty() ) {
             return true;
           } else {
             return false;
           }
       }
   }
   
   
   void building() {
     //buildings
     fill(#9CAD67);
     //second building
     rect(x + 75, 10, 90, 290);
    
     fill(255);
     //windows for second building
     rect(a + 75, 20, 25, 25);
     rect(a + 75, 60, 25, 25);
     rect(a + 75, 100, 25, 25);
     rect(a + 75, 140, 25, 25);
     rect(a + 75, 180, 25, 25);
     rect(a + 75, 220, 25, 25);
     rect(a + 75, 260, 25, 25);
     rect(a + 110, 20, 25, 25);
     rect(a + 110, 60, 25, 25);
     rect(a + 110, 100, 25, 25);
     rect(a + 110, 140, 25, 25);
     rect(a + 110, 180, 25, 25);
     rect(a + 110, 220, 25, 25);
     rect(a + 110, 260, 25, 25);
    
     //first building
     fill(#A52821);
     rect(x, 30, 100, 270);
     x = x - .5;
     a = a - .5;
     windows();
    
     //third building
     fill(#567E98);
     rect(x + 200, 60, 80, 240);
    
     //windows for third building
     fill(255);
     rect(a + 195, 70, 15, 15); //first column
     rect(a + 195, 90, 15, 15);
     rect(a + 195, 110, 15, 15);
     rect(a + 195, 130, 15, 15);
     rect(a + 195, 150, 15, 15);
     rect(a + 195, 170, 15, 15);
     rect(a + 195, 190, 15, 15);
     rect(a + 195, 210, 15, 15);
     rect(a + 195, 230, 15, 15);
     rect(a + 195, 250, 15, 15);
     rect(a + 195, 270, 15, 15);
     rect(a + 218, 70, 15, 15); //second column
     rect(a + 218, 90, 15, 15);
     rect(a + 218, 110, 15, 15);
     rect(a + 218, 130, 15, 15);
     rect(a + 218, 150, 15, 15);
     rect(a + 218, 170, 15, 15);
     rect(a + 218, 190, 15, 15);
     rect(a + 218, 210, 15, 15);
     rect(a + 218, 230, 15, 15);
     rect(a + 218, 250, 15, 15);
     rect(a + 218, 270, 15, 15);
     rect(a + 240, 70, 15, 15); //third column
     rect(a + 240, 90, 15, 15);
     rect(a + 240, 110, 15, 15);
     rect(a + 240, 130, 15, 15);
     rect(a + 240, 150, 15, 15);
     rect(a + 240, 170, 15, 15);
     rect(a + 240, 190, 15, 15);
     rect(a + 240, 210, 15, 15);
     rect(a + 240, 230, 15, 15);
     rect(a + 240, 250, 15, 15);
     rect(a + 240, 270, 15, 15);
    
     //animate background moving
     //stop movement when blob gets to smoke stack
     if(x<800) {
       x = x - .5;
       a = a - .5;
     }
   }
   
   void windows() {
     //windows for first building
     fill(255);
     rect(a, 50, 25, 25);
     rect(a, 90, 25, 25);
     rect(a, 130, 25, 25);
     rect(a, 170, 25, 25);
     rect(a, 210, 25, 25);
     rect(a, 250, 25, 25);
     rect(a + 40, 50, 25, 25);
     rect(a + 40, 90, 25, 25);
     rect(a + 40, 130, 25, 25);
     rect(a + 40, 170, 25, 25);
     rect(a + 40, 210, 25, 25);
     rect(a + 40, 250, 25, 25);
    
   }
   
   void ground() {
     //sidewalk
     noStroke();
     fill(#C1BFBD);
     rect(0, 300, 1300, 50);
    
     //ground in front of sidewalk
     fill(#399543);
     rect(0, 350, 1300, 50);
   }
   
   void blob() {
   }
   
   void draw() {
     background(255);
     fireW1.run();
     fireW1.addParticle();
     ground();
     building();
    
     blob();
   
   }
   

Wow that was much simpler than I expected >.> Thank you so much! :P

How would I go about making the animation stop at a certain point. What would I put inside an "if" statement? Then I could just put the translate at (0, 0) within the "if" statement, correct?

Awesome, it works! Thanks again. :D