Modified equation of 2-D model equation PDE

Question

I have the following 2-D model equation $$a\frac{\partial u}{\partial x}+b\frac{\partial u}{\partial y}=0, a=\cos(\phi),b=\sin(\phi),0<\phi<\frac{\pi}{2}.$$ I have an equidistant finit-volume grid with $\Delta x=\Delta y=h$. I end up with the discretization equation: $$a(u_{i,j}-u_{i-1,j})+b(u_{i,j}-u_{i,j-1})=0.$$ My task now is to determine the modified equation of the discretization equation. From what I have understood I should use Taylor expansions of $u_{i-1,j}$ and $u_{i,j-1}$ to determine the modified equation. I am however unsure what the correct Taylor expansions of these are. My guess is that they should be $$u_{i-1,j}=u_{i,j}-h\frac{\partial u_{i,j}}{\partial x}+\frac{h^{2}}{2}\frac{\partial^{2}u_{i,j}}{\partial x^{2}}-\frac{h^{3}}{6}\frac{\partial^{3}u_{i,j}}{\partial x^{3}}$$ $$u_{i-1,j}=u_{i,j}-h\frac{\partial u_{i,j}}{\partial y}+\frac{h^{2}}{2}\frac{\partial^{2}u_{i,j}}{\partial y^{2}}-\frac{h^{3}}{6}\frac{\partial^{3}u_{i,j}}{\partial y^{3}}$$ But then each expansion only contains either $x$ or $y$ partial derivatives. Could someone help me by telling me if my guess is wrong here, and if so what it should be?