Some commonly used linear functions in economics are the demand functions, supply functions, inverse demand, and inverse supply functions, budget lines, isocost lines, average revenue functions, marginal revenue functions, consumption and saving functions, aggregate demand function, IS and LM, etc., though many of these functions can also be non-linear. Generally, marginal cost and average cost functions are U-shaped (not your shape though). However, there are cases when marginal, and average cost functions are also linear. Linear functions in economics have all the usual properties of linear functions; except that, in some cases, economic variables cannot be negative, i.e., the domain is restricted. For example, quantity, price, capital, labor, etc. cannot be negative. We cannot consume a negative amount, no way! Some economic variables, however, can take negative values. If you drink 10 Coca-Cola in a party in just one hour, most likely the marginal utility of the 10th Coca-Cola will be a huge negative number.
We discuss the examples from demand curve and the budget constraint in the practice question section, but please remember that if you can identify the dependent and independent variables, all linear functions follow the similar properties while calculating their slopes and intercepts and sketching their graphs.