A key characteristic of indifference curves derived from a quasi-linear utility function is that they are vertical shifts of one another. This can be demonstrated by expressing the indifference curve equation as a function of consumption, $c$, in terms of free time, $t$. For two different utility levels, $u_1$ and $u_0$, the vertical distance between their respective indifference curves at any given value of $t$ is calculated as $(u_1 - v(t)) - (u_0 - v(t))$, which simplifies to the constant value $u_1 - u_0$. Since this vertical distance does not depend on $t$, the curves are parallel in the vertical direction.