Question

Find the equation of the line perpendicular to y=-1/2x-5 that passes through the point (2,7) Write this line in slope-line intercept

Answer 1

y = 2x + 3

Explanation:

the equation of a line in slope- intercept form is

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

y = -
`(1)/(2)` x - 5 ← is in slope- intercept form

with slope m = -
`(1)/(2)`

given a line with slope m then the slope of a line perpendicular to it is

`m_(perpendicular)` = -
`(1)/(m)` = -
`(1)/(-(1)/(2) )` = 2 , then

y = 2x + c ← is the partial equation

to find c substitute (2, 7 ) into the partial equation

7 = 4 + c ⇒ c = 7 - 4 = 3

y = 2x + 3 ← equation of perpendicular line