How would i move from one point to another along the line y=2/3x+1

The equation is written in slope intercept form
y= mx + b with m= slope and b= y-intercept

so in your equation 
y=2/3x + 1,
the slope is 2/3 and the y-intercept is (0,1)

slope is also known as rise/run

so to move from one point to another, starting at (0,1) (since you know that point is on the line) you would move up 2 units and to the left 3 units.

hope this helped!