Finding a Parameter for Parallel Lines

The line passing through $(2, 0)$ and $(-2, 6)$ is parallel to the line passing through $(k,\, 2k-1)$ and $(6, 7)$. What is the value of $k$? The answer is in the form $\frac{\alpha}{\beta}$ where $\alpha$ and $\beta$ are coprime positive integers. Input the value of $\alpha + \beta$.