Which of the following is the equation of a line perpendicular to the line y=-10×+1 passing through the point (5,7)

Y = -10x + 1...slope here is -10. A perpendicular line will have a negative reciprocal slope. To find the negative reciprocal of a number, flip the number and change the sign. So our perpendicular line will need a slope of 1/10.

y = mx + b
slope(m) = 1/10
(5,7)x = 5 and y = 7
now sub and find b, the y int
7 = 1/10(5) + b
7 = 1/2 + b
7 - 1/2 = b
14/2 - 1/2 = b
13/2 = b

so ur perpendicular line going thru (5,7) is y = 1/10x + 13/2