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It is false that in an energy diagram for a chemical reaction, energy is plotted along the x-axis (the horizontal axis) and reaction progress is plotted along the y-axis (the vertical axis). The energy is actually plotted along the y-axis and the reaction along the x-axis.
It is because of this activation energy that we first need to show an increase in energy from the reactant to the activated complex and then a decrease in energy from the activated complex to the product. We show this on the energy graphs by drawing a curve from the energy of the reactants to the energy of the products.