Question

what is the equation of a line that passes through the point (6,1) and perpendicular to the line whose equation is 2x+y= - 6 ?

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 )

rearrange 2x + y = - 6 into this form

subtract 2x from both sides

y = - 2x - 6 ← 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)`

y =
`(1)/(2)` x + c ← is the partial equation

to find c substitute (6, 1) into the partial equation

1 = 3 + c ⇒ c = 1 - 3 = - 2

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