Question

Which statement is true about the graphs of the two lines y= -8x-5/4 and y= 1/8x+4/5?

A. The lines are perpendicular to each other because –8 and 1/8 are opposite reciprocals of each other.

B. The lines are perpendicular to each other because -5/4 and 4/5 are opposite reciprocals of each other.

C.The lines are neither parallel nor perpendicular to each other because –8 and 1/8 are not opposite reciprocals of each other.

D. The lines are neither parallel nor perpendicular to each other because -5/4 and 4/5 are not opposite reciprocals of each other.

Answer 1

The lines are perpendicular to each other because
`-8` and
`(1)/(8)` are opposite reciprocals of each other.

Explanation:

The first line has equation
`y=-8x-(5)/(4)`.

The slope of this equation is
`-8`.

The second equation is
`y=(1)/(8)x+(4)/(5)`

The slope of this equation is
`(1)/(8)`

The two slopes are negative reciprocals of each other.

This means that the two lines are perpendicular.