Someone do this for 25 points ?

Option C.

Step-by-step explanation:

Slope of the line passing through (1, 1) and (0, 2)

m =

m =

m = -1

Equation of the line passing through point (1, 1) and slope = -1,

y - y' = m(x - x')

y - 1 = (-1)(x - 1)

y - 1 = -x + 1

y = -x + 2

This piece of function is true for x ≤ 1

Similarly, slope of the line passing through two points (1, -1) and (2, -3),

m' =

    = -2

Equation of the line passing through (1, -1) and slope = -2

y + 1 = (-2)(x - 1)

y + 1 = -2x + 2

y = -2x + 1

This piece of function is true for x > 1

Therefore, Option C. will be the answer.