Step 1: Recall the rate law for a first order reaction.
For a first order reaction the rate is directly proportional to the concentration of the reactant, so \(\text{rate} = k[A]\). This is a straight-line relation of the form \(y = mx\).
Step 2: Decide what is plotted on each axis.
If we take rate on the y-axis and concentration \([A]\) on the x-axis, then comparing with \(y = mx\) we see the slope is \(k\) and the constant term is zero.
Step 3: Predict the shape of the graph.
Because the constant term is zero, the line must pass through the origin (0,0). It rises evenly as concentration increases, giving a straight line going up to the right.
Step 4: Rule out the wrong shapes.
A zero order reaction would give a flat horizontal line (rate does not change with concentration), and a curved line would mean the order is not one. So those graphs are not correct.
Step 5: Match with the options.
The only graph that is a straight line passing through the origin matches Graph (A).
\[ \boxed{\text{Graph (A)}} \]