Question

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

Answer 1

see explanation

Explanation:

The equation of a line in slope- intercept form is

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

y = - 4x - 1 ← is in slope- intercept form

with slope m = - 4

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

`m_(perpendicular)` = -
`(1)/(m)` = -
`(1)/(-4)` =
`(1)/(4)`, thus

y =
`(1)/(4)` x + c ← is the partial equation of the line

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

2 = -
`(1)/(2)` + c ⇒ c =
`(5)/(2)`

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