A change in the supply of a good sericauses a shift in the supply curve.

This statement is WRONG.

The supply curve is an upward-sloping function that determines the relationship between price and quantity supplied. Therefore, if the quantity supplied changes, this would trigger a movement along the curve (and not a shift!).

An increase in the quantity supplied corresponds to an increase in the selling price of the product. Producers are willing to supply larger quantities when the price is higher. This proves why the slope of the curve is positive. On the contrary, a decrease in the quantity supplied corresponds to a decrease in the price.