How did the House of Bourbon descend from King Louis IX of France?

The House of Bourbon is a branch of the house of Capet, which served as the third race of French kings. The dynasty traces its lineage back to King Louis IX through his sixth son, Robert, comte de Clermont.1

Robert de Clermont married the heiress of the lordship of Bourbon, and this lordship was elevated to a duchy for his son, Louis I, in 1327. Consequently, Louis I—the grandson of Louis IX—is recognized as the founder of the house of Bourbon. While the "direct line" of the Capetian dynasty ended in 1328, the Bourbons eventually ascended to the French throne in 1589 following the extinction of the house of Valois male line, adhering to the Salic Law of Succession.12