First we get 2x - y = 3 into slope-y-intercept form y = mx + b
by solving it for y

       2x - y = 3

Add -2x to both sides

           -y = 3 - 2x

Divide through by -1

            y = -3 + 2x

Reverse the order of the terms on the right

            y = 2x - 3

Now we can compare that to

            y = mx + b

and see that its slope is m = 2 and its
y-intercept is b = -3. We don't need its
slope but we do need its y-intercept b = -3

This means the the line that we are looking for
also crosses the y-axis at the point (0, -3).  
That means the problem is now this one:

Find the equation of the line that passes
through the two points (-4, 2) and (0, -3).
We use the slope formula:

     y2 - y1
m = --------- 
     x2 - x1
           
where (x1, y1) = (-4, 2) 
and (x2, y2) = (0, -3)

     (-3) - (2)     -5
m = ------------ = ----- = -5/4 
     (0) - (-4)      4

Then we can either use the point-slope
formula 

y - y1 = m(x - x1)

or the slope-y-intercept

y = mx + b

either way we end up with 

y = -5/4x - 3

To put this in standard form, we

1. Clear of fractions

2. Get the x term first, the y term
   second, the equal sign third, and
   the constant term fourth.

3.  If the x term has a negative
    coefficient, multiply through by 
    -1 to make it positive.

y = -5/4x - 3

Multiply through by 4

4y = -5x - 12

Add 5x to both sides

5x + 4y = -12

Edwin