Answer: (y - 2) = - ¹/₄ (x - 10)
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)