Calculate the slope of a line passing through the intersection of two lines Let say I have this figure,

I know slope $m_1$, slope $m_1$, $(x_1, y_1)$, $(x_2, y_2)$ and $(x_3, y_3)$. I need to calculate slope $m_3$. Note the line with $m_3$ slope will always equally bisect line with $m_1$ slope and line with $m_2$.

You have $m_1=\frac{Y_2-Y_1}{X_2-X_1}=\tan(\alpha_1)$ and $m_2=\frac{Y_3-Y_1}{X_3-X_1}=\tan(\alpha_2)$, so you'll get 
$$m_3=\tan(\alpha_2+\frac{\alpha_1-\alpha_2}{2})=\tan(\frac{\alpha_1+\alpha_2}{2}).$$
