According to wiki, regarding elliptic curve points addition, the following formula for the slope holds
$$s = \frac{y_Q-y_P}{x_Q-x_P}$$ where $P(x_P,y_P)$ and $Q(x_Q,y_Q)$ are distinct points on the curve $y^2 = x^3 + ax + b \pmod q$, $q$ odd prime.
I do know that $$s = \frac{y_Q-y_P}{x_Q-x_P} = (y_Q-y_P)\cdot(x_Q-x_P)^{-1} \pmod q$$
At my university, my teacher said that we can avoid the computation of the multiplicative inverse $(x_Q-x_P)^{-1}$ using projective coordinates (i.e. avoiding using the Extended Euclidean Algorithm). For example each affine point $M(x_M,y_M)$ in the projective coordinates has the form $M(x_M,y_M,1)$.
My question : Could you provide me an example of how to do this?