HOW TO GRAPH LINEAR FUNCTIONS

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


How to graph it?


1. To graph a function such as f(x) = y = 2x + 7, we can select a table of values, plot and connect the points. To fill the table, we choose values for x and use the function to get the values of y as shown in the following table.

x	-3.5	-2	-1	0	0.5	1	2>
y	0	3	5	7	8	9	11

The graph of the data in the above table is:

The value of y when x is zero in the function is called the y-intercept and the value of x when y is zero is called the x-intercept. For more information on intercepts, please refer to intercepts

The above graph is a linear function of the form

y = mx + c

where m is the slope of the straight line and c is the y-intercept.
The slope of a straight line passing through two points (x₁, y₁) and (x₂, y₂) is defined as following:

m = ( y₂ - y₁ )/(x₂ - x₁)

For the above graph, slope = 2 and the y-intercept = 7.