Question

Find the equation of a line perpendicular to x−5y=4 that contains the point (−1,2). Write the equation in slope-intercept form

Answer 1

y = - 5x - 3

Explanation:

The equation of a line in slope- intercept form is

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

Given

x - 5y = 4 ( subtract x from both sides )

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

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

with slope m =
`(1)/(5)`

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

`m_(perpendicular)` = -
`(1)/(m)` = -
`(1)/((1)/(5) )` = - 5 , then

y = - 5x + c ← is the partial equation

To find c substitute (- 1, 2) into the partial equation

2 = 5 + c ⇒ c = 2 - 5 = - 3

y = - 5x - 3 ← equation of perpendicular line