Please check my answer thank you ×ω×
dont mind the tabs i have open

y = (1/2)x - 9/2

==========================================================

Explanation:

The equation y+2x = 1 solves to y = -2x+1 after subtracting 2x from both sides.

That second equation is in the form y = mx+b

The slope in this case is m = -2. Flip the fraction and flip the sign to get 1/2.

The original slope is -2 and the perpendicular slope is 1/2. The two slopes multiply to -1.

We'll use this new slope as the m value, along with the coordinates (7,-1) to solve for b like so:

y = mx+b

-1 = (1/2)*7+b

-1 = 3.5+b

-1-3.5 = b

-4.5 = b

b = -4.5

b = -9/2

Since m = 1/2 and b = -9/2, this means we go from y = mx+b to y = (1/2)x-9/2 which is choice C

The graph is below.