4x + 3y = 12   

We must get it in the slope-y-intercept form: y = mx + b.

We subtract 4x from both side:

 4x + 3y = 12
-4x            -4x
-------------------
      3y = 12 - 4x

We swap the terms on the right because the form y = mx + b has the x term first

      3y = -4x + 12

We divide all three numbers by 3

      y = x + 

Simplify

       y = x + 4   

Next we compare that to

       y = mx + b   which has slope m and y-intercept (0,b)

We can see that m =  and that b = 4 so the y-intercept
is the point (0,4)

The graph is below.  Notice that the y-intercept is the point (4,0)
That's where the line crosses the y-axis. Notice that it goes 
downhill as you move to the right. That tells us that the slope  is
a negative number. Notice that it rises up to 4 (the numerator of the
slope) on the y-axis, and that it runs out to 3 (the denominator of the
slope) on the x-axis.



Edwin