The total velocity of our <x, y, z, t> vector will always be equal to the speed of light constant, c. You can think of something that has no physical movements as moving forward in time at the speed of light. As x, y, or z increases the magnitude of t will decrease so that the speed of light constant is always achieved.
Why this link has to hold is more complex and I cannot explain it well, but hopefully this gives some insight into time slowing as velocity increases.
I've gone decades without hearing it explained that clearly and simply. Thank you (sincerely).