If y varies directly with x and x increases by 2 is it possible to determine by how much y increases or decreases

Y = kx
y = 2k

it is determine how much the increase of y

Y α x

y = kx

y/x = k = Constant

If x is increased by 2,  (x + 2)

Let the new y, be y₂

Since y/x = constant

y/x = y₂/(x + 2)

(y*(x + 2) )/ x = y₂

(xy +2y) / x  = y₂

y₂ = (xy + 2y) / x

y₂ = (xy)/x  + 2y/x

y₂= y   + 2*(y/x)

Recall the y/x = k

y₂ - y = 2k

y₂ = 2k + y

Therefore the y increases by a value of 2 times the constant of proportionality. 

Hope this explains it.