Equation of given line when velocity is plotted against position with intercept $=v_{0}$ and slope $=v_{0} / x_{0}$ is,
$v=-\frac{v_{0} x}{x_{0}}+v_{0}$ ...(i)
(-Ve sign is became the slope is decreasing)
On differentiating with respect to $t$
$\frac{d v}{d t}=-\frac{v_{0}}{x_{0}} \frac{d x}{d t}+0$
or $a=-\frac{v_{0}}{x_{0}} v$ ...(ii)
Putting $v$ from Eq. (i) in Eq. (ii),
$a =-\frac{v_{0}}{x_{0}}\left[-\frac{v_{0}}{x_{0}} x +v_{0}\right]$
$=\frac{v_{0}^{2}}{x_{0}^{2}} x-\frac{v_{0}^{2}}{x_{0}}$
Which represents a straight line with positive slope and negative intercept.
