Find the equation of the tangent to the curve $y = x^2$ at the point $(2, 4)$.

$\dfrac{dy}{dx} = 2x$, so the gradient at $x = 2$ is 4. Using $y - y_1 = m(x - x_1)$: $y - 4 = 4(x - 2)$, giving $y = 4x - 4$. Using the gradient $x = 2$ itself as the slope gives $y = 2x$.