Answer:
y = (1/2)x + 1
Explanation:
y=mx+b, where m is the slope and b the y-intercept (the value of y when x = 0). We are given y = -2x + 2 as the reference line and are asked to find a line that is perpendicular to it. (We'll get to the (2,2) thing later).
A perpendicular line has a slope that is the negative inverse of the reference line slope, which in this case is -2 (the m). The negative inverse of -2 is -(-1/2) or (1/2), This measn the perpendicular line will have the form:
y = (1/2)x + b
The complication is that we want this new line to go through point (2,2). Easy. Just substitute (2,2) in the aboove ea=quation and solve for b:
y = (1/2)x + b for (2,2)
2 = (1/2)2 + b
b = 2 - 1, b = 1
The equation of the line perpendicular to y = -2x + 2 is y = (1/2)x + 1,
See attached graph for proof.