A lab experiment involves two carts colliding. Cart $1$ has a mass $m_1$ and starts at an initial speed $v,$ while cart $2$ of mass $m_2$ starts at rest. The two carts collide and stick together and the final speed of the carts is after the collision $v_f$ is measured. Many trials of the experiment are performed changing the mass of both carts but keeping the initial speed of cart $1$ constant. Which of the following graphical representations of data would yield a straight line the slope of which is the initial speed of cart $1?$

a$.m_1$ as a function of $m_2{v}_f$

b$.m_2{v}_f$ as a function of $m_1$

c$.m_1$ as a function of $(m_1+m_2)v_f$

d$.(m_1+m_2)v_f$ as a function of $m_1$