write down the equation of a line that is perpendicular to the line y=4x-7 and goes through the point (8,1)

The slope of the perpendicular line to the given one is the negative reciprocal of 4 = -1/4

So we have

y - 1  = (-1/4)(x - 8)  simplify

y - 1 = (-1/4)x + 2     add 1 to both sides

y = (-1/4)x + 3

Here's the graph of both lines......https://www.desmos.com/calculator/4tlynhrbq7