4. In a Cartesian coordinate system, a point whose both vertical and horizontal coordinates are integers is called a lattice point. Then, the minimum distance from all lattice points in the plane to the line $y=\frac{3}{4} x+\frac{2}{3}$ is equal to ( ).
A. 0
B. $\frac{2}{15}$
C. $\frac{4}{15}$
D. $\frac{8}{15}$