Parametrical equations of the straight line

These are simply the vector equation separated by components:$(x,y)=(p_1,p_2)+k\cdot (v_1,v_2)$ $$\left. \begin{array}{rcl} x &=&p_1+k\cdot v_1 \\ y &=& p_2+k\cdot v_2 \end{array}\right \}$$

Find the parametrical equations of the straight line $r$ that crosses the points $(3, 4)$ and $(-2, 6)$.

The vector equation with $A=(3,4)$ and $B=(-2,6)$ is: $$(x, y) = A + k \cdot \overrightarrow {AB} = (3, 4) + k \cdot (-5, 2)$$ Therefore, the parametrical equations of the straight line are: $$\left. \begin{array}{rcl} x=3-5 \cdot k \\ y=4+2 \cdot k \end{array} \right\}$$