Question

Determine the equation of a line through the point (3,-4) that is perpendicular to the line y=3x+7

Answer 1

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

Explanation:

The equation of a line in slope- intercept fprm is

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

y = 3x + 7 is in slope- intercept form

with slope m = 3

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

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

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

To find c substitute (3, - 4) into the partial equation

- 4 = - 1 + c ⇒ c = - 4 + 1 = - 3

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