y = mx + b is slope-intercept form.
(0,b) is the y-intercept, the point where the line crosses the y-axis.
In this graph, the point is (0, -3), which makes b = -3.
Now if you move from (0, -3) to the other point at (1, 1), you'd have move "up 4 and right 1." This makes your slope 4/1 which simplifies to 4.
This tells us m = 4
Putting that all together, you have y = 4x - 3.