First you must know that the slope intercept form is y=mx+b where m is the slope (or rise over run) and b is the y-intercept.
(0,4) and (-3,0) are coordinates for x and y. So first we can already note that the y-intercept (what y equals when x is 0) is 4. So b = 4.
Next we must find the slope, m. Slope is rise over run; or the change of y over the change of x. Let me show you with this problem. We have two x variables and two y variables. X is 0 and -3 and Y is 4 and 0.
4 - 0 = 4
0 - -3 = +3
Okay so on top we have the change of y (4-0) and on bottom is the change in x (0--3) which becomes (0+3) because of the two negative signs. So the slope is positive 4/3. So now we have m and b. All that's left is plugging it in.
Slope-inctercept: y=mx+b ------------ y=4/3x+4
Hope I helped. Feel free to ask questions.