Straight Lines And Pair Of Straight Lines

The points $(2,3)$ and $\left(-4,-\frac{4}{3}\right)$ lie on the opposite sides of the line $L \equiv 5 x-6 y+k=0$ and k is an integer. If the points $(1,2)$ and $(4,5)$ lie on the same side of the line $L=0$, then the perpendicular distance from origin to the line $L=0$ is