Question

Write an equation of a line that is perpendicular to y = 6x + 3 that passes through (−6, 4).

Answer 1

y = -
`(1)/(6)` x + 3

Explanation:

the equation of a line in slope- intercept form is

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

y = 6x + 3 ← is in slope- intercept form

with slope m = 6

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

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

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

to find c substitute (- 6, 4 ) into the partial equation

4 = 1 + c ⇒ c = 4 - 1 = 3

y = -
`(1)/(6)` x + 3 ← equation of perpendicular line