Question

Find the equation of the line passing through point A and perpendicular to AB ?

Answer 1

see explanation

Explanation:

(a ) calculate the slope m using the gradient formula

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

with (x₁, y₁ ) = A(0, 6) and (x₂, y₂ ) = B(3, 0 )

`m_(AB)` =
`(0-6)/(3-0)` =
`(-6)/(3)` = - 2

(b)

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

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

(c)

the equation of a line in slope- intercept form is

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

(0, 6 ) is the y-intercept ⇒ c = 6

y =
`(1)/(2)` x + 6 ← equation of perpendicular line