Answer:
[tex]y=-\frac{1}{4}x-10[/tex]
Step-by-step explanation:
If a line is perpendicular to a line that has slope m, then the slope of the line is -1 / m.
in this case, [tex]y=4x-2[/tex]
∴ [tex]m=4[/tex] by comparing with [tex]y=mx+c[/tex]
the slope of the perpendicular line is
[tex]m=-\frac{1}{4}[/tex]
use the point-slope form: [tex]y-y_{0}=m(x-x_{0} )[/tex]
the equation of the perpendicular line is
[tex]y+11=-\frac{1}{4}(x-4)=-\frac{1}{4}x+1\\y=-\frac{1}{4}x+1-11=-\frac{1}{4}x-10[/tex]
