# Graphical solution of BJT inverter

I have the following BJT inverter circuit and graphs of its electrical characteristics. I need to graphically find the DC response characteristics of this inverter but I don't know how to proceed.

You have circuits equations: $$U_1 = R_1I_b+U_{be}\text{ (I)}$$ $$U_2 = U_{ce} = U_n - R_cI_c\text{ (II)}$$ and $I_c = \beta I_b$
Use the graph to determinate the value of $\beta$ and $U_{be}$. you have $$U_2 = U_n-R_c \beta I_b$$ so $$I_b = \frac{U_n-U_2}{\beta R_c}$$
Introduce $I_b$ in the equation (I) and you get: $U_1=f(U_2)$ with $U_n$, $U_{be}$ and $\beta$ constant.