Assume that f satisfies the differential equation $\frac{∂f}{∂x} = 3 > \frac{∂f}{∂y}$ in the entire plane. Show that f is constant on every line that is parallel with the line $3x + y = 1$.
I feel like in order to show that it is constant, I need show that that partial derivatives are $0$ for lines parallel with the line. But the problem I don't know how to go about doing it, I need a hint.