To find a perpendicular line using the equation of the original line, we just need to transform the slope.
The equation of the original line is:
[tex]y=\frac{x}{4}-4[/tex]So, the slope is 1/4. To get the slope of a perpendicular line, we invert it and change its sign, so the new slope is:
[tex]s=-\frac{1}{\frac{1}{4}}=-4[/tex]With the slope and a point, (-8,5), we can use the slope-intercept form for a line, which is:
[tex](y-y_0)=s(x-x_0)[/tex]Where y0 and x0 are the coordinates of the point. So:
[tex]\begin{gathered} y-5=-4(x-(-8)) \\ y=-4(x+8)+5 \\ y=-4x-32+5 \\ y=-4x-27 \end{gathered}[/tex]