Question

Write an equation of the line that passes through (5. – 1) and is perpendicular to the line y = 1/2x - 1

An equation of the perpendicular line is y =

Answer 1

y = - 2x + 9

Explanation:

The equation of a line in slope- intercept form is

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

y =
`(1)/(2)` x - 1 ← is in slope- intercept form

with slope m =
`(1)/(2)`

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

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

y = - 2x + c ← is the partial equation

To find c substitute (5, - 1 ) into the partial equation

- 1 = - 10 + c ⇒ c = - 1 + 10 = 9

y = - 2x + 9 ← equation of perpendicular line