Question

Find the equation of the line that passes through (-1,2) and is perpendicular to

2y = x − 3
.
Leave your answer in the form
y = mx + c

Answer 1

y = - 2x

Explanation:

The equation of a line in slope- intercept form is

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

Rearrange

2y = x - 3 into this form

Divide all terms by 2

y =
`(1)/(2)` x -
`(3)/(2)` ← 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, hence

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

To find c substitute (- 1, 2) into the partial equation

2 = 2 + c ⇒ c = 2 - 2 = 0

y = - 2x ← equation of perpendicular line