Answer
No, it is not.
Work Step by Step
In order to see if something is a solution to an equation, we plug in the (x,y) point to see if the equality is correct. Thus, we plug (1,1/3) into y=x+2/3 to find:
1/3=1+2/3
1/3=1 2/3
1/3 does not equal 1 2/3, so this is not a solution to the equation.