I don't know the appropriate title, please, if anyone would be so kind to edit it properly, I would appreciate it very much.
if I have a vector $\vec{u}$ and another vector $\vec{v}$, where $\vec{u}$ lies on the line $a: (y = m_ax + c_a)$ and $\vec{v}$ lies on the line $b: (y = m_bx + c_b)$, then does it follow that vector $\vec{u+v}$ lines on line $c: (y = (m_a + m_b) x + c_a + c_b)$?