Being the derivative of a strictly convex function, the function f ′ is strictly monotone and thus injective. The second equation can be solved for x 0 = f ′ ′ − − 1 ( p ) , allowing elimination of x 0 from the first, and solving for the y -intercept b of the tangent as a function of its slope p , b = f ( x 0 ) − − p x 0 = f ( f ′ ′ − − 1 ( p ) ) − − p ⋅ ⋅ f ′ ′ − − 1 ( p ) = − − f ⋆ ⋆ ( p ) where f ⋆ ⋆ denotes the Legendre transform of f .