Question

Write the equation of the line perpendicular to y = 5/3x + 1 that passes through the point (- 8, 2)

Answer 1

y = -
`(3)/(5)` x -
`(14)/(5)`

Explanation:

The equation of a line in slope- intercept form is

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

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

with slope m =
`(5)/(3)`

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

`m_(perpendicular)` = -
`(1)/(m)` = -
`(1)/((5)/(3) )` = -
`(3)/(5)` , thus

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

To find c substitute (- 8, 2) into the partial equation

2 =
`(24)/(5)` + c ⇒ c = 2 -
`(24)/(5)` = -
`(14)/(5)`

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