Use point-slope formula: 

y - y1 = m(x - x1)

y - (-4) = 2 (x - 1)

y + 4 = 2x - 2

y = 2x - 6

point-slope form is: y = mx + b

We're given the slope, m = 2, so: y = 2x + b

We're also given it goes through (1, -4) and those are x and y, since points are given as (x, y). 

Replace the y and x in:

y = 2x + b with -4 and 1:

-4 = 2(1) + b subtract 2 from sides

-4 - 2 = 2(1) + b - 2

-6 = b

Now we know b is -6, can finish the equation y = 2x + b as 

y = 2x - 6