Y-3=3(x+1)

what is the equation in standard form of a parallel line that passes through (0, -3)

First, let's put that line in standard form
y - 3 = 3(x + 1)
y - 3 = 3x + 3
y = 3x + 6

(Standard form is y = mx+b, where m is slope and b is y-intercept.)

Now, a line parallel to that line would have the same slope of 3. So now we have m = 3. Plug that in for m and now we have
y = 3x + b

But we still need the b value. We can get that by plugging in the point (0, -3)
(-3) = 3(0) + b
-3 = 0 + b
b = -3

Now put b back into the equation and your final equation is
y = 3x - 3