Question

What is the equation in slope-intercept form of the line that passes through the point (-1,-1)

and is perpendicular to the line represented by y = 1/2x +5?

Answer 1

y = - 2x - 3

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 + 5 ← 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 , thus

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

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

- 1 = 2 + c ⇒ c = - 1 - 2 = - 3

y = - 2x - 3 ← equation of perpendicular line