Question

Determine whether the line Upper L 1L1 whose equation is yequals=5 x minus 95x−9 and the line Upper L 2L2 whose equation is yequals=one fifth x plus 6 1 5x+6 are​ parallel, perpendicular, or neither.

Answer 1

Neither

Explanation:

Let
`m_(1)` and
`m_(2)` be the gradients of two lines.

1. The two lines are parallel if their gradients
   `m_(1)` and
   `m_(2)` are equal.
2. Two lines are perpendicular if the products of the gradients,
   `m_(1)`
   `m_(2)` =-1, i.e. gradient of one,
   `m_(1)=-(1)/(m_(2))`
   `m_(2)`

Consider the given lines
`L_(1)` whose equation is given as y=5x-9 and the line
`L_(2)` whose equation is given as
`y=(1)/(5)x+6`.

To make a comparison, ensure that the lines are in the slope-intercept form y=mx+c.

In
`L_(1)` y=5x-9,
`m_(1)` =5

In
`L_(2)` ,
`y=(1)/(5)x+6`,
`m_(2)` =
`(1)/(5)`

Their product
`m_(1)`
`m_(2)` = 1,

Therefore the lines are neither parallel nor perpendicular.