Question

Please answer the questions below

Answer 1

see explanation

Explanation:

(3)

Parallel lines have equal slopes

the equation of a line in sloipe- intercept form is

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

y =
`(1)/(4)` x + 5 ⇒ m =
`(1)/(4)`

y = 4x + 5 ⇒ m = 4

y = - 4x + 5 ⇒ m = - 4

y = - 4x - 9 ⇒ m = - 4

the 3rd and 4th options have equal slopes and are parallel

(4)

given a line with slope m then the slope of a line perpendicular to it is

`m_(perpendicular)` = -
`(1)/(m)`

y =
`(1)/(6)` x + 4 ⇒ m =
`(1)/(6)`

y = -
`(1)/(6)` x + 5 ⇒ m = -
`(1)/(6)`

y =
`(1)/(6)` x + 3 ⇒ m =
`(1)/(6)`

y = 6x + 3 ⇒ m = 6

note that a slope of m = 6 , has a perpendicular slope of

`m_(perpendicular)` = -
`(1)/(6)`

the 2nd and 4th lines are perpendicular