A linear equation is a first degree equation in x and y. For example 2x - y = 6 is a linear equation. Graphically a linear equation is represented by a straight line in two dimensional coordinate system. The linear equation when written in the slope - intercept form y = mx + b can be regarded as a linear function f(x) = mx + b, for every input value of x the rule brings out exactly one output.

Any linear equation can thus represent a linear function and the equation can be used to interpret the function.

The slope intercept form of an equation can be regarded as a linear function rule. That is a linear function can be written in the form
f(x) = mx + b where m and b are constants.

For example, the linear equation y = 2x - 3 can be regarded as a linear function f(x) = 2x - 3. Note here the dependent variable can be replaced by the function notation f(x) and the expression 2x -3 is the rule to find the output for the function.

The constant 'm' in f(x) = mx + b gives the rate of change of the function and the 'b' represents the function value when x = 0. In other words f(0) = b.

For the function f(x) = 2x - 3, 2 is the rate of change and f(0) = - 3.

We discuss the significance of theses values and how we use them to write an equation to represent a linear function.