## Convex function

Let $I$ be an open interval where $a. Also, let $f:I\rightarrow \mathbb{R}$ be differentiable.
Prove $f$ is convex if and only if $f(x)\geq f(a)+f'(a)(x-a)$ for all $a,x\in I$.

I have that the definition of convex is $f(x)\leq L(x)$ where $L(x)=f(a)+\frac{f(b)-f(a)}{b-a}(x-a)$

I have tried to switch it around algebraically but I can't seem to figure it out. I'd appreciate any help.