Question

What is an equation of the line that passes through the point (-4,5) and is perpendicular to the line 4x+y=7?

Answer 1

y =
`(1)/(4)` x + 6

Explanation:

the equation of a line in slope- intercept form is

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

given

4x + y = 7 ( subtract 4x from both sides )

y = - 4x + 7 ← 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)` , then

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

to find c substitute )- 4, 5 ) into the partial equation

5 = - 1 + c ⇒ c = 5 + 1 = 6

y =
`(1)/(4)` x + 6 ← equation of perpendicular line