Derive mathematically the first equation of motion $v=u+at?$

Let us consider a body moving with the initial velocity $u$ which have a constant acceleration $a$ and in the time $t$ it the velocity becomes $v$.

As known, Acceleration$=\frac{Change\ of\ velocity}{Time\ taken}$

$a=\frac{v-u}{t}$

Or $at=v-u$

Or $v=u+at$