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.
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.