graph by first solving for y    

   x - 3y = 9

get rid of the "x" term on the left by adding -x to both sides:

   x - 3y = 9
  -x          - x
---------------------
      -3y = 9 - x

Now divide every term by -3:

 =  - 

Simplify:

 =  + 

This is now solved for y. Next we have to 
get some points on the line.

Arbitrarily pick any convenient number to substitute
for x.  I think I will first choose 0 to substitute
for x.  I chose 0 simply because it is easy.  So we 
substitute x = 0

 =  + 
 =  + 
 =  + 
 = 

So one point on the first line is (x, y) = (0,-3) 

Let's plot that point.  That point is on the
y-axis where y = -3

 

Now for the second point on the line, I think I will 
choose 3 to substitute for x.  I chose 3 simply because 
the term  will be  or  so it
won't be a fraction.  I could have chosen any other 
number, but I can avoid fractions by choosing whole
numbers for x that are divisible by 3. So we substitute
x = 3

 =  + 
 =  + 
 =  + 
 = 

So another point on the first line is (x, y) = (3, -2)

Now let's plot that point. It is directly below 3 on
the x axis and directly to the right of -2 on the
y axis:



We could draw a line through those two points.
However to be on the safe side, we should get
a third point. 

Now for the third point on the line, I think I will 
choose -6 to substitute for x.  I chose -6 simply because 
the term  will be  or  so it
won't be a fraction.  I could have chosen any other 
number, but, as before, I can avoid fractions by choosing
whole numbers for x that are divisible by 3. So we 
substitute x = -6

 =  + 
 =  + 
 =  + 
 = 

So another point on the first line is (x, y) = (-6, -5)

Now let's plot that point. It is directly below -6 on
the x axis and directly to the left of -5 on the
y axis:




Now we draw a straight line through all three
points.  



That's the graph of the equation

   x - 3y = 9

Edwin