MAT112 Section Summary: 1.2

Linear Functions and Applications

1. Definitions
   • linear function

     A relationship f defined by

     

     for real numbers m and b. x is called the independent variable while y is called the dependent variable.

   • equilibrium price of a quantity

     the price at which the demand and the supply are equal as functions of price

   • fixed cost

     the costs independent of actual production of items

   • marginal cost

     the cost per unit at a given level of production

   • break-even quantity

     the quantity at which revenue equals cost.

2. Theorems/Formulas

3. Properties/Tricks/Hints/Etc.

4. Summary

   This section is about applications of linear functions, and the interpretation of slope and intercepts in various contexts, including Supply and Demand, Cost analysis, and Break-Even analysis.

   Linear functions are very simple mathematical models, which are often appropriate for initial analyses leading to more complicated models.