Question

Write an equation of the line passing through point P(−8, 0) that is perpendicular to the line 3x−5y = 6.

Answer 1

3x - 5y = 6

-3x -3x

-5y = -3x + 6

`(-5y)/(-5) = (-3x)/(-5) + (6)/(-5)`

`y = (3)/(5)x - (6)/(5)` ⇒ m =
`(3)/(5)`

perpendicular slope (m⊥) =
`-(5)/(3)`

Point-Slope equation:

m =
`-(5)/(3)` (x₁ , y₁)= (-8, 0)

y - y₁ = m(x - x₁)

y - 0 =
`-(5)/(3)`(x - (-8))

y =
`-(5)/(3)`(x + 8)

y =
`-(5)/(3)x - (40)/(3)`