Firstly, find the slope.
Let m = slope
m = (8 - 4)/(1 - 0)
m = 4/1
m = 4
Now use the point-slope formula.
y - y_1 = m(x - x_1)
Pick one of the given points. I will use the point (0, 4) but you can certainly use (1, 8) if you'd like.
We now plug and chug.
y - 4 = 4(x - 0)
y - 4 = 4x
y = 4x + 4
Replace y with f(x).
f(x) = 4x + 4
Did you follow?
