Question

What is the equation in slope-intercept form of a line that is perpendicular to y=2x+2 and passes through the point (4,3)?

(A) y=−12x+5

(B) y=−2x+2

(C) y=2x+3

(D) y=2x+5

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 + 2 ← is 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 (4, 3) into the partial equation

3 = - 2 + c ⇒ c = 3 + 2 = 5

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