Question

a line is perpendicular to y=-2x+5 and intersects the point (-4,2).What is the equation of this perpendicular line

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 )

y = - 2x + 5 ← 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 ← is the partial equation

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

2 =
`(1)/(2)` (- 4) + c = - 2 + c ( add 2 to both sides )

4 = c

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