The figure displays the graph of the x -coordinate of a particle...

The average velocity of a particle is defined as the total displacement divided by the total time taken.

From the given position-time graph:
At $t = 0\text{ s}$, the initial position $x_1 = 0\text{ m}$.
At $t = 10\text{ s}$, the final position $x_2 = 100\text{ m}$.

The displacement of the particle during this time interval is:
$\Delta x = x_2 - x_1 = 100\text{ m} - 0\text{ m} = 100\text{ m}$

The time interval is:
$\Delta t = 10\text{ s} - 0\text{ s} = 10\text{ s}$

The average velocity $v_{\text{avg}}$ is:
$v_{\text{avg}} = \dfrac{\Delta x}{\Delta t} = \dfrac{100}{10} = 10\text{ m/s}$