Find the equation of the tangent to the curve x² + 3y – 3 = 0, which is parallel to the line y = 4x – 5.

finding the slope of the tangent by differentiating the curve

m(tangent) =

equation of tangent is given by y – y₁ = m(tangent)(x – x₁)

now comparing the slope of a tangent with the given equation

m(tangent) = 4

x = – 6

since this point lies on the curve, we can find y by substituting x

6² + 3y – 3 = 0

y = – 11

therefore, the equation of the tangent is

y + 11 = 4(x + 6)