Question

What is the equation of a line perpendicular to y-12=2x-3 that passes through the point (2, 3)?

Answer 1

y = -
`(1)/(2)` x + 4

Explanation:

The equation of a line in slope- intercept form is

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

Given

y - 12 = 2x - 3 ( add 12 to both sides )

y = 2x + 9 ← in slope- intercept 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)`, thus

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

To find c substitute (2, 3) into the partial equation

3 = - 1 + c ⇒ c = 3 + 1 = 4

y = -
`(1)/(2)` x + 4 ← equation of perpendicular line