How can you deduce the order of the reaction with respect to the reagent based on the graph of its concentration against time?

For the zeroth order reaction, the graph would be a straight line with a negative gradient. For the first order reaction, the graph would be a curve with constant half-life. That means the time for the concentration to decrease to the half of its initial value would be constant. For higher orders, the graph would still be a curve but with non-constant half-life.