First, we find the y-intercept, which in this case is -1, because that's where the line crosses the y-axis.
y = mx + b
Where 'm' is the slope and 'b' is the y-intercept, therefore -1 replaces 'b':
y = mx - 1
Now let's take any two points on the line and find the slope.
m = y2-y1/x2-x1
(0, -1) and (1, 2)
m = (2 + 1)/(1 - 0)
m = 3/1
m = 3
So the slope is 3, plug this in the equation also:
y = 3x - 1