Marivs has given a detailed explanation of how to this algebraically. Here is a slightly different way of looking at it from the definitions of slope and $y$-intercept:
You are given the $y$-intercept is -3. From the definition of $y$-intercept a point on the graph is $(0,-3)$.
The defintion of slope is $ \text{slope} = \frac{\Delta y}{\Delta x} = \frac{y_2 - y_1}{x_2 - x_1}$ where $(x_1,y_1)$ and $(x_2,y_2)$ are any two points on the line.
So, if you let $(x_1,y_1) = (0,-3)$, and using the fact that the slope is 3, then any other point on the graph can be obtained by $ 3 = \frac{y - (- 3)}{x - 0}$ so $ y = 3x - 3$
Now, just pick any value of $x$ (other than $0$, since we already have this point, which is the $y$-intercept), and you obtain a second point on the line. Say we let $x=1$, then $y=0$. So connecthing this point $(1,0)$ to the given point $(0,-3)$ you get the graph of this line.