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How to Identify Linear Functions

Algebra is a complex but elegant form of mathematics, one in which variables are used to signify numbers. Algebra first emerged in ancient Egypt and Babylon and its concepts were further developed by the scholars of ancient Greece. There are various types of algebraic functions, including linear, quadratic and cubic. Linear functions are those in which X is raised to the first power. You can identify linear functions both algebraically and graphically.

Instructions

- 1
  Determine the power to which X is raised. A linear function raises X to the first power -- represented as "X to the first" or simply "X."
- 2
  Look at how the equation is written. Linear functions take the form y = mx + b, where m and b are real numbers and x is the variable.
- 3
  Graph the function in question to determine whether it is linear. If it forms a straight line when graphed, it is linear.
- 4
  Plug in any two points on the graph into the equation to verify that it is, in fact, linear. For example, if the line passes the point (2,3), replace x with 2 and y with 3. If these values fit in the equation, you can determine that it's linear.

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