How do enzymes increase the rate of chemical transformation?

(N/A) Enzymes are proteins with a three-dimensional structure that includes an 'active site'. They convert a substrate $(S)$ into a product $(P)$ through the reaction: $S \rightarrow P$.
The substrate binds to the enzyme at its 'active site' to form an $ES$ (Enzyme-Substrate) complex. This complex formation is a transient phenomenon.
During the state where the substrate is bound to the enzyme's active site,a new structure is formed,known as the 'transition state'.
After the bond-breaking or bond-forming process is completed,the product is released from the active site.
The pathway of this transformation goes through the transition state structure. There could be many altered structural states between the stable substrate and the product,all of which are unstable.
If this is depicted graphically,the $Y$-axis represents the potential energy content,and the $X$-axis represents the progression of the reaction.
There is a difference between the energy level of the substrate $(S)$ and the product $(P)$. If $P$ is at a lower energy level than $S$,the reaction is exothermic,and energy does not need to be supplied to form the product.
However,whether the reaction is exothermic (spontaneous) or endothermic (energy-requiring),the substrate must pass through a higher energy state called the 'transition state'.
The difference in the average energy content of the substrate from that of the transition state is called 'activation energy'.
Enzymes increase the rate of reaction by lowering this activation energy barrier,making the transition of $S$ to $P$ easier.