Question

A line is perpendicular to y = -x + 1

and intersects the point (-5,1).
What is the equation of this
perpendicular line?

Answer 1

y = 5x + 26

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

with slope m = -
`(1)/(5)`

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

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

y = 5x + c ← is the partial equation

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

1 = - 25 + c ⇒ c = 1 + 25 = 26

y = 5x + 26 ← equation of perpendicular line