We first plot those two points and draw a line 
through them to find out if it is vertical or
not. The equations of all lines can be placed
in slope-intercept form except the equations
for vertical lines. This is the graph we get:



We see that it is not vertical. So we can proceed
as usual:

We are to find an equation of the line containing 
the points (12,0) and (0,4)

Use the slope formula:

     y2 - y1
m = —————————
     x2 - x1

where (x1, y1) = (12,0) and (x2, y2) = (0,4)

     (4) - (0)      4      -1
m = ——————————— = ————— = ———— = 
    (0) - (12)     -12      3 

Now substitute in the point slope formula:

   y - y1 = m(x - x1)

   y - 0 = (x - (12) )

      y  = (x - 12)

       y = x + 4

That's the equation in the slope-intercept
form because we can compare it with

       y = mx + b

and see that its slope m is  and its
y-intercept (0,b) is the point (0,4)
  
Edwin