Question

What is the slope intercept of a line perpendicular to the line y=2x+3 with the point (-2,-4)

Answer 1

y = -
`(1)/(2)` x - 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 = 2x + 3 is in this form with slope m = 2

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

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

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

To find c substitute (- 2, - 4) into the partial equation

- 4 = 1 + c ⇒ c = - 4 - 1 = - 5

y = -
`(1)/(2)` x - 5 ← equation of perpendicular line