Step-by-step explanation:
Two straight lines are perpendicular when the product of their slopes is -1.
the given line is [tex]y=9-\frac{x}{5}[/tex].
The slope of line [tex]y=mx+c[/tex] is [tex]m[/tex].
So, the slope of [tex]y=9-\frac{x}{5}[/tex] is [tex]\frac{-1}{5}[/tex].
Let slope of perpendicular line be [tex]m[/tex].
[tex]m\textrm{ x }\frac{-1}{5}=-1[/tex]
[tex]m=5[/tex]
The line also passes through [tex](-2,-2)[/tex].
The equation of line is [tex](y-(-2))=5(x-(-2))[/tex].
[tex]y+2=5x+10[/tex]
∴ [tex]y=5x+8[/tex] is the line perpendicular to [tex]y=9-\frac{x}{5}[/tex] and passing through [tex](-2,-2)[/tex].
