Two things: Call background() every frame, and redraw everything on the screen every frame.
The way that you're display right now, which involves drawing two rectangles to the screen, copying that to a PImage, and displaying that every frame is completely unnecessary...

calsign Im sorry but I dont completely understand. Could you change the code where I need to change it. I tried a few different ways but I still had it writing on top of the other data.
Thanks Ken

To reiterate, there are a couple of things that you need to do:

• Remove graphBGround and all references to it... it is completely unnecessary.
• Button, RectButton, and squares (this class should start with a capital letter) should all be one class. Merge all of the drawing functions... and anything else that is necessary. All of your RectButtons should become this new class, and your squares should be wrapped into it as well.
• You are now displaying everything on every frame (as you should be), and you need to call background() at the beginning of draw() to erase everything from the previous frame.
  

Thanks calsign Ill try to get it to work with your comments. Below is my code for the overall program Im trying to get it to work with. Im using serial data from a arduino to create 3 graphs for a accelerometer. I started first by just graphing the data which worked well without having a graph behind it. My Graph class is set up so I can use 1-3 graphs all depending on the number that I want to display, and position then create a background image.  In my draw() I would dispaly the background image and then the serial data would be above updating as the serial data came in. But since the data some times is to large for the graph I added 4 sensitivity buttons that would adjust the data. This also works well. But know I want to change the Y axis data to update the change in sensitivity. I commented the serial input so the program works without the serial data.
Am I going about this the correct way ?
Or should I try to create a graph class that also has the serial data updated in the class with the graph behind it ? then in draw() redraw the graph.display with the serial data in for each frame.

Sorry for all the info and questions but Im semi new to programming this is the largest program I have attempted.

Thanks again Ken

below is the graphing program

//Program parameters

Graph xGraph,yGraph,zGraph,allGraphs;

//Window Size
int wWidth = 700;
int wHeight = 700;
int sideBoarder = 30;
int topBorder = 25;
int bottomBorder = 100;
int innerWindowWidth = wWidth-sideBoarder*2;
int innerWindowHeight = wHeight-topBorder-bottomBorder;
int gSpacing=35;
//Image of graph that will be in background below serial line graph
PImage graphBGround;

//Serial parameters
import processing.serial.*;
//Serial and line graph data
Serial myPort;
//X,Y,Z accelerometer values
int valueX=0;
int valueY=0;
int valueZ=0;
//String data from serial
int lf = 10;
String stringToChange="";
//Save data points to graph each redraw
int[] valueXs = new int[int(innerWindowWidth-gSpacing*2)];
int[] valueYs = new int[int(innerWindowWidth-gSpacing*2)];
int[] valueZs = new int[int(innerWindowWidth-gSpacing*2)];

int gScale=1;

// button parameters
RectButton rect1, rect2, rect3, rect4;
boolean locked = false;
color offColor = color(255,0,0);
color onColor = color(0,255,0);

void setup(){
  // try{
  String portName = Serial.list()[0];
 // myPort = new Serial(this, portName, 9600);
 // myPort.bufferUntil(' ');
 // }
 // catch(NullPointerException e){
 // }
  size(int(wWidth), int(wHeight));
  rect(sideBoarder,topBorder,innerWindowWidth,innerWindowHeight);


 
  textAlign(CENTER);
  fill(0);
  text("Accelerometer Data", wWidth/2, topBorder-5);
 
  xGraph = new Graph(3,1,"X-Graph Data",sideBoarder,topBorder,innerWindowWidth,innerWindowHeight);
  yGraph = new Graph(3,2,"Y-Graph Data",sideBoarder,topBorder,innerWindowWidth,innerWindowHeight);
  zGraph = new Graph(3,3,"Z-Graph Data",sideBoarder,topBorder,innerWindowWidth,innerWindowHeight);

  createGImage();
 
  rect1 = new RectButton("Sen X1",wWidth/2-100, innerWindowHeight+50, 50, 30, offColor, onColor);
  rect2 = new RectButton("Sen X2",wWidth/2-50, innerWindowHeight+50, 50, 30, offColor, onColor);
  rect3 = new RectButton("Sen X4",wWidth/2, innerWindowHeight+50, 50, 30, offColor, onColor);
  rect4 = new RectButton("Sen X8",wWidth/2+50,innerWindowHeight+50, 50, 30, offColor, onColor);
 
}

void createGImage(){
  xGraph.showGraph();
  yGraph.showGraph();
  zGraph.showGraph();
  graphBGround = get();
}
void changeGraph(int GScale){
 
   
}
void draw(){
  image(graphBGround, 0, 0);
 
 
  strokeWeight(1);
  beginShape();//show X line graph
  stroke(255, 0, 0);
  noFill();
  for (int i = 0; i<valueXs.length;i++) {
    vertex(i+gSpacing+sideBoarder+1,valueXs[i]/gScale+xGraph.gHcenter()+topBorder);
  }
  endShape();
  beginShape();//show Y line graph
  stroke(0, 255, 0);
  noFill();
  for (int i = 0; i<valueYs.length;i++) {
    vertex(i+gSpacing+sideBoarder+1,valueYs[i]/gScale+yGraph.gHcenter()+topBorder);
  }
  endShape();
  beginShape();//show Z line graph
  stroke(0, 0, 255);
  noFill();
  for (int i = 0; i<valueZs.length;i++) {
    vertex(i+gSpacing+sideBoarder+1,valueZs[i]/gScale+zGraph.gHcenter()+topBorder);
  }
  endShape();
 
  update(mouseX, mouseY);
  rect1.display();
  rect2.display();
  rect3.display();
  rect4.display();
}


void update(int x, int y)
{
  if(locked == false) {
    rect1.update();
    rect2.update();
    rect3.update();
    rect4.update();
  }
  else {
    locked = false;
  }

  if(mousePressed) {
    if(rect1.pressed()) {
      rect1.basecolor = onColor;
      rect2.basecolor = offColor;
      rect3.basecolor = offColor;
      rect4.basecolor = offColor;
      gScale = 1;
    } else if(rect2.pressed()) {
      rect1.basecolor = offColor;
      rect2.basecolor = onColor;
      rect3.basecolor = offColor;
      rect4.basecolor = offColor;
       gScale = 2;
    } else if(rect3.pressed()) {
      rect1.basecolor = offColor;
      rect2.basecolor = offColor;
      rect3.basecolor = onColor;
      rect4.basecolor = offColor;
       gScale = 4;
    } else if(rect4.pressed()) {
      rect1.basecolor = offColor;
      rect2.basecolor = offColor;
      rect3.basecolor = offColor;
      rect4.basecolor = onColor;
      zGraph.setScale(8);
      createGImage();
       gScale = 8;
    }
  }
}



void serialEvent(Serial myPort) {
 
  //Serial data until new line
  stringToChange = myPort.readStringUntil(' ');
  if (stringToChange != null) {//split X,Y,Z data that has a tab betweein
    String [] data = split(stringToChange, ' ');
    //trim string data and convert to ints
    valueX = int(data[0].trim());
    valueY = int(data[1].trim());
    valueZ = int(data[2].trim());
    // shift all values in array by 1 to free up the new data
    for (int i = 1; i<valueXs.length;i++) {
      valueXs[i-1] = valueXs[i];
      valueYs[i-1] = valueYs[i];
      valueZs[i-1] = valueZs[i];
    }
    //replace new data at last array point and scale if needed
    valueXs[valueXs.length-1]=valueX;
    valueYs[valueYs.length-1]=valueY;
    valueZs[valueZs.length-1]=valueZ;
  }
}


class Graph{
  String gNqme;
  int nGraphs;
  int gPosition;
  int graphH;
  int graphW;
  int wHash;
  int xPosition;
  int yPosition;
  int gHcenter;
  int gSens;

  void setxPosition(int x){this.xPosition=x;}
  void setyPosition(int y){this.yPosition=y;}
  void setScale(int ScaleSize){this.gSens=ScaleSize;}
  public int getGraphH(){return graphH;}
  public int getGraphW(){return graphW;}
  public int gHcenter(){return gHcenter;}

  Graph(){
  }
  int gSpacing=35;
 
  Graph(int numberGraphs, int P, String Name, int X, int Y,int W,int H){
    nGraphs = numberGraphs;
    gNqme = Name;
    gPosition = P;
    xPosition=X;
    yPosition=Y;
    graphW = W-gSpacing*2;
    graphH= (H-gSpacing*(1+nGraphs))/nGraphs;
    wHash=30;
    gSens =1;
  }
 
  void showGraph(){
    pushMatrix();
    translate(xPosition,yPosition);
    rectMode(CENTER);
    stroke(0);
    fill(255);
    switch(gPosition) {
      case 1:
        rect(graphW/2+gSpacing,graphH/2+gSpacing,graphW,graphH);
        createGrid(gSpacing,graphH/2+gSpacing,graphW,graphH+gSpacing);
        break;
      case 2:
         rect(graphW/2+gSpacing,graphH/2+gSpacing*gPosition+graphH,graphW,graphH);
         createGrid(gSpacing,graphH/2+gSpacing*gPosition+graphH,graphW,graphH*2+gSpacing*2);
        break;
      case 3:
        rect(graphW/2+gSpacing,graphH/2+gSpacing*gPosition+graphH*2,graphW,graphH);
        createGrid(gSpacing,graphH/2+gSpacing*gPosition+graphH*2,graphW,graphH*3+gSpacing*3);
        break;
    }
    popMatrix();
  }
  void createGrid(float x1,float y1, float x2, float y2){
        PFont font1,font2;
        font1 = createFont("ArialNarrow-Bold-10", 12);
        font2 = createFont("ArialMT", 14);
        int a=int(graphH/2/30);
        int k=0;
        fill(0);
        textFont(font1, 12);
        text("Seconds", wHash,y2+gSpacing/2); 
        for(int i=a;i>(-a-1);i--){
                  if(i==0){//Left graph Names
                    rotate(radians(-90));
                    textFont(font2, 14);
                    textAlign(CENTER);
                    text(gNqme,-(y1+30*i),gSpacing-5);
                    rotate(radians(90));
                  }
            stroke(225);
            //Horiz lines
            line(x1+1,y1-30*i,x2+gSpacing-1,y1-30*i);
            fill(0);
            textAlign(CENTER);
            textFont(font1, 12);
            text(i*60/gSens, graphW+x1+15,y1-30*i+5);
            if(i*30 ==0){
              gHcenter=int(y1-30*i);
            }
            int b=int(graphW/wHash);
            //X hashes Lines and Numbers
            for(int j=0;j<b;j++){
                 textAlign(CENTER);
                 if(k==0){
                     if(j%4==0){
                      text(j*wHash, x1+x2-j*wHash,y2+gSpacing/2);
                     }
                 }
                 if(j!=0){
                      line( x1+x2-j*wHash,y1-30*i+5, x1+x2-j*wHash,y1-30*i-5);
                 }
            }
            k++;  
        }
  }
 
}

class Button
{
  String Name;
  int x, y;
  int sizeX;
  int sizeY;
  color basecolor, highlightcolor;
  color currentcolor;
  boolean over = false;
  boolean pressed = false;  

  void update()
  {
    if(over()) { currentcolor = highlightcolor;
    }
    else { currentcolor = basecolor;
    }
  }

  boolean pressed()
  {
    if(over) {
      locked = true;
      currentcolor = highlightcolor;
      return true;
    }
    else {
      locked = false;
      currentcolor = basecolor;
      return false;
    }   
  }

  boolean over()
  {
    return true;
  }

  boolean overRect(int x, int y, int width, int height)
  {
    if (mouseX >= x && mouseX <= x+width &&
      mouseY >= y && mouseY <= y+height) {
      return true;
    }
    else {
      return false;
    }
  }
}


class RectButton extends Button
{
  RectButton(String A,int ix, int iy, int xsize,int ysize, color icolor, color ihighlight)
  {
    Name = A;
    x = ix;
    y = iy;
    sizeX = xsize;
    sizeY = ysize;
    basecolor = icolor;
    highlightcolor = ihighlight;
    currentcolor = basecolor;
  }

  boolean over()
  {
    if( overRect(x, y, sizeX, sizeY) ) {
      over = true;
      return true;
    }
    else {
      over = false;
      return false;
    }
  }

  void display()
  {
    stroke(0);
    fill(currentcolor);
    rectMode(CORNER);
    rect(x, y, sizeX, sizeY);
    fill(0);
    textAlign(CENTER);
    text(Name,x+sizeX/2,y+sizeY/2+5);
  }
}

This is becoming... quite confusing...

Why don't you just display the graphs every frame? This is the preferred method, and it gets rid of the need to use your image... and it's what I've been trying to say the entire time.

If the buttons are used to scale the graphs... wouldn't it be simpler to have the graphs scale themselves based on the data? I don't know what they look like... but, again, this is preferred. There was a post that I answered that covered the issue of scaling... it involves finding the largest element in the data and scaling everything else so that the largest element fits within the view...

Thanks again calsign I'll try to change my method as you suggested thanks again for the help.