Write an equation of the line that passes through (3,8) and is perpendicular to the line y=5x-4

For lines perpendicular to a line you find the negative reciprocal of the gradient of that line in this case it is -0.2 or -1/5
Then you substitute the new gradient and the point into the equation of a line
8=-0.2(3) +c
8=-0.6+c
8.6=c
After wards you substitute only the gradient and the y intercept in the line eq’n
Y=-0.2x+8.6