Question

Determine whether the pair of lines y = 6x - 4 and x - 6y = -10 are parallel, perpendicular, or neither.

Answer 1

neither

Explanation:

• Parallel lines have equal slopes

• The product of the slopes of perpendicular lines is - 1

the equation of a line in slope- intercept form is

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

given

y = 6x - 4 ← in slope- intercept form

with slope m = 6

given

x - 6y = - 10 ( subtract x from both sides )

- 6y = - x - 10 ( divide through by - 6 )

`(-6)/(-6)` y =
`(-1)/(-6)` x -
`(10)/(-6)` , that is

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

with slope m =
`(1)/(6)`

Now 6 ≠
`(1)/(6)` , so lines are not parallel

and 6 ×
`(1)/(6)` = 1 ≠ - 1 , so lines are not perpendicular