Find an equation of the tangent line to the graph of y = g(x) at x = 3 if g(3) = −2 and g'(3) = 6. (Enter your answer as an equation in terms of y and x.)

Answer 1

You know the slope must be

m = g'(3) = 6

You know the tangent point is (3,-2). You have enough information to write the equation of the line in point slope form:

y - y₁ = m(x - x₁)

y - (-2) = 6(x - 3)

y + 2 = 6(x - 3)