Study Notes on Graphing Linear Functions and Economics

Introduction to Linear Functions and Graphing

  • Concepts involved in graphing linear functions and determining key points like equilibrium.

Graphing Linear Functions

  • Essential practice in graphing linear functions in specified domains.

Example of Graphing

  • Starting from a domain, we graph the function.
  • Use of open circles to indicate points not included in the graph (e.g., at 9,700).
  • Calculate specific values (e.g., the value at (39, 475)) using a calculator for precision.

Adjusted Gross Income and Tax Calculation

  • The relationship established between adjusted gross income and tax bill.
  • The statement “adjusted gross income at x value” suggests the x-axis represents income in dollars.
  • The function indicates that the tax bill corresponds to this gross income (tax bill = adjusted gross income).

Supply and Demand in Economics

  • Quantity Supplied (S) and Quantity Demanded (D) for cell phones represented by equations:
    • S=30p−900S = 30p - 900
    • D=−7,500,000+28.50pD = -7,500,000 + 28.50p
  • Where pp is the price in dollars.

Part A: Finding the Equilibrium Price

  • Definition of equilibrium: where quantity supplied equals quantity demanded.
  • Set up the equation:
    • Solve for pp by setting S=DS = D.
    • Rearranging equation leads to:
    • 30p−900=−7,500,000+28.50p30p - 900 = -7,500,000 + 28.50p
  • Combining like terms results in: