Implicit Derivative at a Point

Question

If xy + 3 - 4y = 0 then find the equation of all tangent lines to the curve when x = 5

Answer 1

When x = 5, we have 5y + 3 - 4y = 0. So, y = -3.

xy + 3 - 4y = 0

Differentiating implicitly with respect to x, we get: y + x(dy/dx) - 4(dy/dx) = 0.

So, dy/dx = y / (4-x) = -3 / (4 - 5) = 3 = slope of tangent line

Equation of tangent line: y + 3 = 3(x - 5)

Simplify to get y = 3x - 18