How do you determine a linear function from a table and graph?

You are
asking how to determine a linear function from a table and a graph.

Linear
functions graph as a straight line, no curves allowed. So, if the graph is a straight line, it
is the graph of a linear function.

From a table, you can verify a linear
function by examining the x and y values.  The rate of change for y with respect to x remains
constant for a linear function. This rate of change is called the slope.

We'll use this table for the example.

x        y

0        2

1        3

2        4

3        5

4        6

In this example the rate of
change between the x and y values is always 2.  This function could be written with the linear
equation y = x + 2.

A linear function graphs as a straight
line.

A table of values for a linear function
shows a constant rate of change between the x and y values.