Answer
$y=-6$
Work Step by Step
Use: $m=\displaystyle \frac{\text{change in y}}{\text{change in x}}=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}.$
The product of slopes of perpendicular lines is $-1,\quad$ $(m_{1}=-\displaystyle \frac{1}{m_{2}} ).$
The slope of the line passing through $(-1,-2)$ and $(4,-1)$ is
$m_{1}=\displaystyle \frac{-1-(-2)}{4-(-1)}=\frac{1}{5}$
The line passing through $(-2,y)$ and $(-4,4)$ has the slope
$m_{2}=\displaystyle \frac{4-y}{-4-(-2)}=\frac{4-y}{-2}=\frac{y-4}{2}$
Since the lines are perpendicular,
$m_{1}\cdot m_{2}=-1$
$\displaystyle \frac{1}{5}\cdot(\frac{y-4}{2})=-1\qquad $... multiply with $10$,
$y-4=-10\qquad $... add 4
$y=-6$
