Question

I don't know how to do this please help. Thank you

Find the equation of a line that passes through the point (4,2) that is perpendicular to the line y = 4/3 x. Show your work.

Answer 1

Let y =
`(4)/(3)` x be L₁ & the unknown be L₂

Now, if L₂ is perpendicular to L₁ then the product of their gradient (m) is -1. This implies that the gradient of L₂ is the negative reciprocal of L₁:

∴ if m of L₁ =
`(4)/(3)`

then m of L₂ =
`- (3)/(4)`

Now since L₂ passes through the line (4, 2),

then by using the point-slope form (y - y₁) = m (x - x₁)
⇒ (y - 2) =
`- (3)/(4)` (x - 4)
⇒ 4 (y - 2) = -3 (x - 4)
⇒ 4y - 8 = -3x + 12
⇒ 4y + 3x = 20

∴ the line that passes through the point (4,2) that is perpendicular to the line y = 4/3x is characterized by the equation 4y + 3x = 20