Determine whether the graphs of the given equations are parallel, perpendicular, or neither.

y=x+12

Y=-x+1

Choose the correct answer below.

a. neither

b. parallel

c. perpendicular

Answer: c perpendicular

Step-by-step explanation:

y=x+12 y=mx+b m=1 slope 1

Y=-x+1 m=-1 slope - 1

slopes are perpendicular obviously, or

(1, y (1)) - (0, y (0)) = (1,13) - (0,12) = (1,1)

(1, Y (1)) - (0, Y (0)) = (1,0) - (0,1) = (1,-1)

(1,-1) dot (1,1) = 1*1+1*-1 = 0 therefore perpendicular.

Two vectors are perpendicular if and only if their dot (inner) product is zero, or the projection of one onto the other is zero, or if the cosine of the angle between them is zero.