Question

Does someone mind helping me with this problem? Thank you!

Answer 1

y = -
`(1)/(4)` x - 10

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 - 2 ← 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)` , then

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

to find c substitute (4, - 11 ) into the partial equation

- 11 = -
`(1)/(4)` (4) + c = - 1 + c ( add 1 to both sides )

- 10 = c

y = -
`(1)/(4)` x + (- 10) , that is

y = -
`(1)/(4)` x - 10 ← equation of line