Question

Write the equation of the line, in slope intercept form, that is perpendicular to 3x+6y=18 passing through the point (-4,2). Show your work.

Answer 1

y = 2x + 10

Explanation:

the equation of a line in slope- intercept form is

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

given

3x + 6y = 18 ( subtract 3x from both sides )

6y = - 3x + 18 ( divide terms by 6 )

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

with slope m = -
`(1)/(2)`

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

`m_(perpendicular)` = -
`(1)/(m)` = -
`(1)/(-(1)/(2) )` = 2 , then

y = 2x + c ← is the partial equation

to find c substitute (- 4, 2 ) into the partial equation

2 = - 8 + c ⇒ c = 2 + 8 = 10

y = 2x + 10 ← equation of perpendicular line