Question

What is an equation of the line that is perpendicular to 3x+y=−5 and passes through the point (3, −7) ?

Answer 1

y =
`(1)/(3)` x - 8

Explanation:

the equation of a line in slope-intercept form is

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

rearrange 3x + y = - 5 into this form

subtract 3x from both sides

y = - 3x - 5 ← in slope-intercept form

with slope m = - 3

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

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

`m_(perpendicular)` = -
`(1)/(-3)` =
`(1)/(3)`

y =
`(1)/(3)` x + c ← is the partial equation

to find c substitute (3, - 7 ) into the partial equation

- 7 = 1 + c ⇒ c = - 7 - 1 = - 8

y =
`(1)/(3)` x - 8 ← equation of perpendicular line