Question

Write the equation of a line that is perpendicular to the given line and that passes through the given point. y= 2/3x + 9 ; (–6, 5)

Answer 1

y = -
`(3)/(2)` x - 4

Explanation:

The equation of a line in slope- intercept form is

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

y =
`(2)/(3)` x + 9 ← is in slope- intercept form

with slope m =
`(2)/(3)`

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

`m_(perpendicular)` = -
`(1)/(m)` = -
`(1)/((2)/(3) )` = -
`(3)/(2)`, thus

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

To find c substitute (- 6, 5) into the partial equation

5 = 9 + c ⇒ c = 5 - 9 = - 4

y = -
`(3)/(2)` x - 4 ← equation of perpendicular line