Question

What is the equation of a line that contains the point (2, 1) and is perpendicular to the line y= 3x - 4

Answer 1

see explanation

Explanation:

The equation of a line in slope- intercept form is

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

y = 3x - 4 ← 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)`, hence

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

To find c substitute (2, 1 ) into the partial equation

1 = -
`(2)/(3)` + c ⇒ c =
`(5)/(3)`

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