What is the equation of the line perpendicular to y= -2x+5 that passes through the point (2,
2)?

y = 1/2x + 1

Explanation: for a perpendicular line, take the reciprocal of the given slope. In this case, the reciprocal of -2 is +1/2.
Plug your new slope into the equation
Y = Mx+b
And then plug in the given (2,2) for the x and y coordinates. And solve for b.

Y = 1/2x + b
2 = 1/2(2) + b
1 = b

You have the new slope that we got from taking the reciprocal of the given slope, and we found our b. The equation of line perpendicular to y = -2x + 5 is:

y = 1/2x + 1