what is the equation of a line perpendicular to the line y=-10x+1 passing thru point (5,7)

To find a line perpendicular, use the opposite-reciprocal slope of the line given. Also, use the point-slope form of a line since you're given a point.

y-7 = 1/10 (x-5)

Simplify to y=mx+b (slope-int) form

y-7= 1/10x -1/2
y = 1/10x + 13/2