Question

Find an equation of the line perpendicular to y = - 2x + 2

Answer 1

Answer:

y = (1/2)x + 1

Step-by-step 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.