Question

Write an equation for the perpendicular line to the line whose equation is 4y-5x=20 that contains the point (-2,-3)

Answer 1

4x + 5y = - 23

Explanation:

the equation of a line in slope-intercept form is

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

rearrange 4y - 5x = 20 into this form

add 5x to both sides

4y = 5x + 20 ( divide all terms by 4 )

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

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

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

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

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

y = -
`(4)/(5)` x + c ← is the partial equation

to find c substitute (- 2, - 3) into the partial equation

- 3 =
`(8)/(5)` + c ⇒ c = -
`(23)/(5)`

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

multiply all terms by 5

5y = - 4x - 23 ( add 4x to both sides )

4x + 5y = - 23 ← in standard form