Question

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 1

Answer: c perpendicular

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.

Answer 2

They are perpendicular

Explanation:

These lines are in fact perpendicular when plotted, and actually have a intersection point of (-5 1/2, 6 1/2)