# Parallelogram on the Coordinate Plane

Geometry Level 4

A parallelogram on the coordinate plane is defined by the following lines: $\left\{\begin{array}{l}y=4x+5 \\ y=4x+3 \\ y=nx+5\\ y=nx+3\end{array}\right.$

If the area of the parallelogram is $$16$$, then $$n$$ can be expressed as $$\dfrac{p}{q}$$, where $$p,q$$ are coprime positive integers. Find the smallest possible value of $$p+q$$.

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