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.
