Question

Find the equation of the line that

is perpendicular to y =1/6 x + 3
and contains the point (-3,23).​

Answer 1

y = - 6x + 5

Explanation:

The equation of a line in slope- intercept form is

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

y =
`(1)/(6)` x + 3 ← is in slope- intercept form

with slope m =
`(1)/(6)`

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

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

y = - 6x + c ← is the partial equation of the perpendicular line.

To find c substitute (- 3, 23) into the partial equation

23 = 18 + c ⇒ c = 23 - 18 = 5

y = - 6x + 5 ← equation of perpendicular line