Question

Find an equation for line perpendicular to 2x+6y=18 and goes through the point (8,-1)

Answer 1

y = 3x - 25

Explanation:

The equation of a line in slope- intercept form is

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

Given

2x + 6y = 18 ( subtract 2x from both sides )

6y = - 2x + 18 ( divide terms by 6 )

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

with slope m = -
`(1)/(3)`

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

`m_(perpendicular)` = -
`(1)/(m)` = -
`(1)/(-(1)/(3) )` = 3 , then

y = 3x + c ← is the partial equation

To find c substitute (8, - 1 ) into the partial equation

- 1 = 24 + c ⇒ c = - 1 - 24 = - 25

y = 3x - 25 ← equation of perpendicular line

Answer 2

3x +y = -2

Explanation:

First of all, it is helpful to put the given equation in standard form. We can do that by dividing it by 2 to eliminate the common factor from the numbers.

x -3y = 5

Next, since you want the perpendicular line, you can swap the coefficients of x and y, and negate one of them. This can give you ...

3x +y = (some constant)

The constant will be found using the given point.

3x +y = 3(2) +(-8) = -2 . . . the perpendicular line

An equation is ...

3x +y = -2