what is the meaning

if you take into account two different variables, e.g. the number of ice-cream scoops and the amount of money they cost, we say they are directly proportional because 2 scoops cost twice the amount of money 1 scoop costs.
1 scoop costs 1 dollar, 2 scoop cost 2 dollars, 3 scoop cost 3 dollars......

roger?

inchoate

being a physicist the two concepts suggest the followings to me, variable means a quantity, like time, which can assume any value of a certain set.
time E R+ is a variable when we observe motions in kinematics.
in quantummechanics distinct means, for example, that energy levels of particles (electrons...) can assume only certain quantum values, opposite of being continual..

Children get apples. The apples are so hard that it is impossible to cut them into two, three,.....
How many apples may a child have when the basket is empty?
The number of apples a child may have are distinct values: 1,2,3,4,5,6,... depending on how many apples originally there were in the basket.
Distinct means a child can not have 1.3, 7.6, etc. apples because not any one

In mathematical context "distinct" also means "not identical", e.g. two distinct values = two well-defined values or states differing from each other.

In mathematical terms, "directly proportional" means the two variables follow a linear equation with an intercept of zero (i.e. the line passes through the origin 0,0).

Kajjo

y=ax, then y and x are directly proportional.
y=a/x inversely proportionate

incho