How does demand curve for labor change when there is a proportional payroll tax on employer
Your guess that somewhat is happening with the slope was a good one. The slope will indeed change. If you want to draw that new Demand line ($D_1$) it has to start at the exact same point of the old demand line (if wages are zero the percantage tax will be zero too). The correct intersection with the Y-Axis would be: $(1-t) W_0$ (this simply means one minus the tax rate ($t$) times the old intersection point ($W_0$). I also made a little graph: