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.