Question 513312
<pre>
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

      {{{3/3}}}y = {{{(-4)/3}}}x + {{{12/3}}}

Simplify

       y = {{{-4/3}}}x + 4   

Next we compare that to

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

We can see that m = {{{-4/3}}} 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 {{{-4/3}}} 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.

{{{drawing(400,400,-5,5,-3,7,graph(400,400,-5,5,-3,7,(-4/3)x+4),
locate(.2,4.2,"(0,4)")
)}}}

Edwin</pre>