parallel perpendicular lines

Question

Prove whether the lines are parallel, perpendicular, or neither. Show your work and explain your reasoning.

x+y=1 4x+4y=1

Answer 1

x + y = 1

4x + 4y = 1

 

Examine the slopes.  If they are the same, the lines are parallel.  If their product is -1, the lines are perpendicular.

 

x + y = 1 ⇒ y = -x + 1 ⇒ m₁ = -1

4x + 4y = 1 ⇒ y = -x + 1/4 ⇒ m₂ = -1

 

m₁ = m₂ ⇒ the lines are parallel