Question

Are the following lines parallel, perpendicular or neither? 5y - x = 5 5y - x = -5 a Parallel b Perpendicular c Neither

Answer 1

Parallel lines

Explanation:

Parallel lines have equal slopes

The product of the slopes of perpendicular lines equals - 1

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y-intercept )

Rearrange the 2 equations into this form and compare slopes

5y - x = 5 ( add x to both sides )

5y = x + 5 ( divide all terms by 5 )

y =
`(1)/(5)` x + 1 ← in slope- intercept form

with slope m =
`(1)/(5)`

5y - x = - 5 ( add x to both sides )

5y = x - 5 ( divide all terms by 5 )

y =
`(1)/(5)` x - 1 ← in slope- intercept form

with slope m =
`(1)/(5)`

Since slopes are equal then the lines are parallel