Bisecting a Parallelogram

Geometry Level 4

Let \(A = (0,0)\), \(B = (2,4)\), \(C = (17,4) \) and \( D = (15,0)\). Then \(ABCD\) is a parallelogram. A line through the point \( (0,-1) \) divides the parallelogram into two regions of equal area. The slope of this line can be written as \(\frac{a}{b} \) where \(a\) and \(b\) are positive coprime integers. Find \(a+b\).

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