Question

Write the equation of a line perpendicular to 8xplus5yequals2 that passes through the point ​(2​,negative 7​).

Answer 1

8x + 5y = 2   →   5y = - 8x + 2   →   y = (-8/5)x + 2  ⇒ m = -8/5

perpendicular slope = 5/8

Point-Slope formula: y - y₁ = m(x - x₁)  ; where (x₁, y₁) is the given point

y - (-7) = (5/8)(x - 2)

y + 7 = (5/8)(x - 2)

8(y + 7) = 5(x - 2)

8y + 56 = 5x - 10

8y + 66 = 5x

        66 = 5x - 8y   ⇒   5x - 8y = 66

Answer: 5x - 8y = 66