The Slutsky equation is a way to look at how changes in one variable can affect another. For example, it can help us understand how an increase in the price of an item (variable 1) affects how much of the item people buy (variable 2).
Say we have a market with lots of different items. Each item has a different price, which affects how much of that item people buy. The Slutsky equation helps us understand how a change in one item's price (variable 1) affects the amount of items people buy (variable 2).
When the price of an item goes up (variable 1), people buy less of that item. This means that the amount of money people are spending on that item goes down (variable 2). The Slutsky equation helps us show this mathematically. Basically, it shows us how one variable (like the price of an item) affects another ( like how much of an item people buy).