The component form of a vector is written as a coordinate pair whose $x\text{-}$ and $y\text{-}$values determine the horizontal and vertical change, respectively. The horizontal change is given by the difference between the $x\text{-}$value of the initial point and the $x\text{-}$value of the terminal point. Similarly, the vertical change is given by the difference between the $y\text{-}$value of the initial point and the $y\text{-}$value of the terminal point.