linear function


Definition of Linear Function

  • A function that can be graphically represented in the Cartesian coordinate plane by a straight line is called a Linear Function.

More about Linear Function

  • A linear function is a first degree polynomial of the form, F(x) = m x + c, where m and c are constants and x is a real variable.
  • The constant m is called slope and c is called y-intercept.

Examples of Linear Function

  • y = 3x + 5 is a linear function.
  • The graph of the function y = 2x is shown below. This is a linear function since the points fit onto a straight line.

Solved Example on Linear Function

Identify the graph that represents a linear function.

Choices:
A. Graph 1
B. Graph 3
C. Graph 4
D. Graph 2
Correct Answer: C
Solution:
Step 1: The graph of a linear function is a straight line.
Step 2: Graph 4 is a straight line.
Step 3: So, Graph 4 represents a linear function.

Related Terms for Linear Function

  • Cartesian Coordinates
  • Coordinate Plane
  • Function
  • Plane
  • Straight Line