Businesses, or at least profit-maximizing ones, may change their prices due to taxes, depending on what type of tax it is; it's very hard to pass along an income tax.
A sales tax or unit tax can be passed along to the degree that consumers will still buy at the higher price (demand doesn't change much based on price). These tend to be commodity-type products (bread, plastic deck chairs, cotton T-shirts), where the price is set through relatively strong competition, would go up if all sellers faced a new tax.
A sales tax on something more unique, like oil paintings, sailboats, and high-quality furniture would not necessarily make customers willing to pay more for them - price is already more a function of demand than actual costs (there may be competition, but only a few sellers are capable of supplying the market, so profits tend to be higher).
In the first case, most of the tax is paid by the consumer in the form of a price increase. In the second case, most of it is paid by the seller, because the price can't really be increased (in fact, for a large tax, the seller may have to decrease their price to keep the same total cost, and number of customers).
An income tax *might* be passed along in the same way, but it would require most or all of the competitors to raise prices without colluding in order to do so; given the abstractness of 'ownership' in most companies, it's likely this wouldn't happen, qt least quickly.