Interpolation of function that includes a step change (discontinuous)

Question

I have the following function that includes a step change:

function image

For those who cannot access the image, the function is linear between two times $t_1$ and $t_2$ with gradient $m_a$, there is a step-change at point $t_2$, then is linear between times $t_2$ and $t_3$ with gradient $m_b$. $t_1$ and $t_3$ have values $x_1$ and $x_3$, and for $t_2$: the start of the step-change is $x_{2a}$ and the end of the step change is $x_{2b}$.

The variables I know are: $t_1$, $t_2$, $t_3$, $x_1$, $x_3$, and the magnitude of the step change (ie. $(x_{2b} - x_{2a})$). I do not know the values of any other variables.

Are the degrees of freedom low enough so that interpolation (linear or any other type) is possible, or do I not know the values of enough variables? If it is possible, how?

Thanks.

Note: this might hold the answer but it'll use language and symbols etc. that are way above my level.

EDIT: I should have noted: $m_a\neq m_b$