Write an equation in slope-intercept form for the line that passes through (4, -10) and is Perpendicular to the line Y = x + 8.

If it is perpendicular to $y=x+8$, the slope must be $-1$, so the equation for the line is $y=-x+c$ for some c. Substituting $(4,-10)$, we get $-10=-(4)+c$, so $c=-6$. The equation of the line is $\boxed{y=-x-6}$