For a certain reaction R arrow Product, the plot of concentration...

From the given graph, the plot of concentration $[R]$ versus time $t$ is a straight line with a negative slope.

The equation for this straight line can be written as:
$y = mx + c$
$[R] = (\text{slope}) \times t + \text{intercept}$

Given that the intercept is $[R_0]$ and the slope is $-k$, the equation becomes:
$[R] = -kt + [R_0]$

This equation represents the integrated rate law for a zero-order reaction. For a zero-order reaction, the rate of reaction is independent of the concentration of the reactant:
$\text{Rate} = -\dfrac{d[R]}{dt} = k[R]^0 = k$

Integrating both sides:
$\int_{[R_0]}^{[R]} d[R] = -k \int_0^t dt$
$[R] - [R_0] = -kt$
$[R] = -kt + [R_0]$

Since the graph matches this equation, the order of the reaction is $0$.

Answer: $0$