The given graph shows the& variation of velocity with displacement....

The v - x equation from the given graph can be written as

$v = ( - \dfrac{{v}_{0}}{{x}_{0}} )x + {v}_{0}$... (i)

$a = \dfrac{d v}{d t} = ( - \dfrac{{v}_{0}}{{x}_{0}} )\dfrac{d x}{d t}$

$= ( - \dfrac{{v}_{0}}{{x}_{0}} )v$

Substituting v from Eq. (i) we get,

a = ( - \dfrac{{v}_{0}}{{x}_{0}} ) [ ( - \dfrac{{v}_{0}}{{x}_{0}} )x + {v}_{0} ]

$a = {( \dfrac{{v}_{0}}{{x}_{0}} )}^{2}x - \dfrac{{v}_{0}^{2}}{{x}_{0}}$
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Thus, a-x graph is a straight line with positive slope and negative intercept.
Correct answer is