Question

Find the equation perpendicular to y=-2x+10 through (10,7)

Answer 1

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

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 + 10 ← 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 of the perpendicular line

to find c substitute (10, 7 ) into the partial equation

7 = 5 + c ⇒ c = 7 - 5 = 2

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