Question

Five the equation of line that is perpendicular to f(x)=-2x+1 that goes through point (0,5)

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 )

f(x) = - 2x + 1 ← 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)` =
`(1)/(2)` , then

y =
`(1)/(2)` x + c

the line crosses the y- axis at (0, 5 ) ⇒ c = 5

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