Question

He equation of line m is 4x+5y=?2. What is the slope of a line that is perpendicular to line m? Enter your answer in the box.

Answer 1

perpendicular slope =
`(5)/(4)`

the equation of a line in slope-intercept form is

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

rearrange 4x + 5y = 2 into this form

subtract 4x from both sides

5y = - 4x + 2 ( divide all terms by 5 )

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

with slope m = -
`(4)/(5)`

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

`m_(perpendicular)` = -
`(1)/(m)` = - 1 /-
`(4)/(5)` =
`(5)/(4)`