Question

Are the lines 4x-y-5=0 and x+4y+1=0 perpendicular

Answer 1

Yes

Explanation:

4x-y-5=0

4x-4x-y-5=0-4x

-y-5=-4x

-(y+5)=-4x

y+5=4x

y=4x-5 ==> slope: 4

x+4y+1=0

x-x+4y+1=0-x

4y+1=-x

4y=-x-1

y=(-x-1)/4

y=-x/4 -1/4 ==> slope: -1/4

4*(-1)=-4

-4 * ? = 1

-4/(-4) * ?=1/(-4)

?=-1/4 √

Since the slopes of the lines are opposite reciprocals, the lines are perpendicular.