The law of energy conservation states that the total energy of any body is the same regardless its state of movement or its position is space. This means that for a projectile that is launched from the ground (altitude 0 m) the sum of kinetic and potential energies is the same.
`Ek +Ep = constant`
or written in terms of projectile speed and height
`m*v^2/2 + m*g*h = constant`
where the value of the constant can be determined by knowing that at Hmax there is only potential energy and at H=0 (where V= V0) there is only kinetic energy
`constant = m*g*Hmax = m*g*V_(0)^2/2`
Now we can see the dependence of kinetic energy on height h
`Ek = constant - m*g*h = m*g*(Hmax-h)`
Therefore Ek has a linear dependence on h. See figure below for its graph.