Answer :
The line is perpendicular to the line:
[tex]y=\frac{1}{5}x-1[/tex]so the new slope will be the inverse reciproc of the other line so the new slope will be:
[tex]m=-5[/tex]now we ca unsa the formula of the slope an the coordinate (4, -2) to find the equation:
[tex]m=\frac{y-y_1}{x-x_1}_{}[/tex]and we replase m and the coordinate so
[tex]-5=\frac{y-(-2)}{x-4}[/tex]and we solve for y
[tex]\begin{gathered} y+2=-5x+20 \\ y=-5x+20-2 \\ y=-5x+18 \end{gathered}[/tex]