Alright, this is kind of like working backwards.
We have a slope of 34. And the slope formula is m = y1 - y2 / x1 - x2.
34 = (-4 - -1) / (4 - k)
34 = -3 / (4 - k)
34(4 - k) = -3
136 - 34k = -3
-34k = -139
I believe that k = 139/34, or 4.09 approximately. Hope this helps!