Linear Functions

Linear Functions

A linear function is an algebraic equation in which each term is either a constant or the product of a constant and the first power of a variable. A function is a relation with the property that each input is related to exactly one output and a relation is a set of ordered pairs. The graph of this function is a straight line and the vertical line is not the graph of a function.

 Linear functions are written as equations and are characterized by their y-intercept and slope. It is those whose graph is a straight line.

A linear function having the following form

y = f(x) = a + bx

It has one independent variable and one dependent variable. x is the independent variable and they are dependant variables. Here a is the constant term or the y-intercept. The coefficient of the independent variable is b. It is also called the slope and gives the rate of change of the dependent variable.

A linear function is of the form f(x) = mx + b where ‘m’ and ‘b’ are real number .Here,

• • ‘m’ is the slope of the line
  • ‘b’ is the y-intercept of the line
  • ‘x’ is the independent variable
  • ‘y’  is the dependent variable

Linear Function Equation and Examples

The linear function is f(x) = x, which is a line passing through the origin.A linear function equation is f(x) = mx + b 

Examples.

• • f(x) = 3x – 2
  • f(x) = -5x – 0.5
  • f(x) = 3

Also, read the Equations containing two variables