Question

Passes through (10,2), perpendicular to y = 4x + 6

Answer 1

Answer:     (y - 2) = - ¹/₄ (x - 10)

Step-by-step explanation:

When two lines are perpendicular, the product of their slope/gradient = -1. Another way of thinking of this is that they are negative-reciprocal of each other.

Let y = 4x + 6 be [a]  & the perpendicular line [b]

     since the slope of [a] = 4

      then the slope (m) of [b] = - ¹/₄

Since we know the slope of [b], we can use the point-slope form (y - y₁) = m (x - x₁);     where (x₁ , y₁) = (10 , 2)  &  m =   - ¹/₄

∴ the equation of the perpendicular line :   (y - 2) =  - ¹/₄ (x - 10)