Understanding elliptic curve point addition over a finite field
Your coordinates are elements of the finite field. For a point $P = (x_p, y_p)$ with $x_p,y_p \in \mathbb{F}_n$, where $\mathbf{F}_n$ is the finite field of order $n$ over which the elliptic curve is defined.

Since $n$ is prime, your slope will also be an element of the field $\mathbb{F}_n$. Even if $n$ was composite and $\gcd(x_q - x_p, n) = 1$, $\lambda$ is still an element of your field since an inverse of $(x_q - x_p)$ would still exist in this case. To compute the slope, you must find the multiplicative inverse of $(x_q-x_p)$ in your field $\mathbb{F}_n$. Then 
$$\lambda \equiv (y_q - y_p)\cdot(x_q - x_p)^{-1} \pmod n \text.$$