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.
Example 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
Video Examples: Graphing Linear Functions by Finding X,Y Intercept
Solved Example on Linear Function
Ques: Identify the graph that represents a linear function.
- A. Graph 1
- B. Graph 3
- C. Graph 4
- D. Graph 2
Correct Answer: C
- 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.